Speaking from my experiences, primarily in the 7 range... First part is my rambling thoughts, at the bottom is a more to the point answer.
Neutering didn't quite function as I expected from previous major versions. Neutering a system will not dramatically impact the potential reinforcements of a system to the point at which you can just forget about it. Fleetships can still reinforce to the point at which clearing it out again will still be quite difficult, especially if they're clustered around fewer points. The time to get there may vary, but 500 unis among five different in-system locations can be easier than 300-400 between just a couple.
The most dramatic impact of neutering nowadays seems to be the elimination of guardians and their spawn points.
I'm a bit vague on the current reinforcement logic (I should probably turn on the logging to understand that better), but a key thing to keep in mind (and sorry if it sounds obvious) when neutering is not just AI progress, but rather the fact that the more planets are not under AI control, the more reinforcements the AI will get. Experience: The AI will pay dramatically more attention to reinforcing the systems on alert. Wiki: The AI will not reinforce to non-alerted planets unless all the alerted planets are full up (I don't know if this information is still current after the introduction of barracks, homeworlds will get reinforced some even when not alerted for instance).
This means neutering a planet works wonderfully, until it doesn't. Then it goes to hell. With my playstyle, this will go to hell most often on an X-map. Simple map types have enough connections to provide plenty of alerts, snake types have few enough connections you're dealing with threatballs anyways, but X-maps often have that one system with a nuclear eye you just don't want to deal with right now.
If you have four systems, and neuter four adjacent mark iv worlds, it will be a huge help, especially if you need to move through those systems frequently. If you have ten or fifteen systems, a mark iv on your flank will be a major pain, especially if it is out of your way and tends to be forgotten, unlike one enroute to the AI homeworlds. You'll reach a certain tipping point where it will suddenly become a nightmare or hassle around the time of a CPA.
I always recommend neutering systems of low value enroute to your destinations, but out of the way systems like Hermes are the ones that always come back to bite me later on. Neuter them, but try not to base plans around having them permanently present adjacent to your backlines, you'll regret it. With the Fallen Spire hunger for territory, you'll create especially antagonistic reinforcements.
On the other hand, taking Hel (I presume the P9 is in ARS) is a fantastic idea, even if it antagonizes two mk4s you then have to neuter. Why? Because it puts more systems on alert (to dilute reinforcements) than it contributes to the reinforcement pool, and odds are great that they'll be connected to your front line (making it convenient to clear them out) and that you'll want to travel through them, making clearing out fleetships less of an inconvenience, and easier without the hassle of guardians.
The other thing to consider is Core Shield Generators. Patrols can be a hidden difficulty boost to the future clearing out of a system you've neutered now, especially if they favor gravity drains, tackle launchers, or maws. The recent fix does a lot to make early patrols more reasonable, but Fallen Spire conquests should cause patrols counts to skyrocket.
Let me run a theoretical scenario for you.
You flip every system adjacent to your homeworld. You'll be contributing five planets to the reinforce calcs, but you'll be alerting eight planets. Fleet ships won't reinforce these systems too heavily, but they will reinforce them. If you neuter a mark four planet immediately after putting it on permanent alert, it should go relatively easily barring a prolonged battle such that a turtle might give you. Mark two ships should be able to easily overwhelm less than a hundred mark four ships + guardians. If those fleet ships start getting into the three-hundred range and you're still stuck with mark two ships, that plus the guardians will make clearing that system expensive. If you clear out the guard post now, it is much safer to later on bring your starships in support of the fleet. Bomber Starships will make handling Spire Maws and Tractor Platforms easier, but if their pursuit antagonizes a laser guardian, they can go down quickly. Plasma Siege Starships are a help dealing with gravity drains and slower low-cap units, but they're not as exposed. If you neuter all the adjacent mark IV shortly after colonizing the AI system, they'll be pretty painless and most importantly, remain so.
If you claim those four worlds, neuter the adjacent mark ivs, and then proceed to flip all the planets to your northeast (Licho, Semmelwiss, Coco, Leibniz), the additional AIP, the 8 conquests to 6 alerted ratio will be a lot less friendly to you. Consolidating your territory to natural chokepoints can backfire if your borders are mkIV planets, and your fleetship tech stays low-tech (which is tempting if you haven't found a factory). Even neutered, those planets will start to become a hassle to you, and get worse as you push out further.
On the other hand, if I ignored my natural tendency to seize a large swath of territory with only a few entry points, then you will find me taking those five planets, neutering the adjacent ones, and relying on a combination of logistics commands, riot starships, and possibly spider turrets and zenith spacetime manipulators (a must for mini-ram lovers) then you'll find me taking a different strategic approach which will start the same (neutering the MkIVs) but result in a much longer period of time before those neutered MKIVs become concern. For example, you might find me killing one of the four: Eve, Hades, Isaac, Ares, while I neutering all the rest. This will put a couple more planets on alert, but my scouts will reach further out, deep strikes will be avoided, I may spot a Factory, Civilian Spire, Data Center, Fabricator, Dyson Sphere, etc. While this is going on, the Mark IVs I previously neutered won't be running horribly out of control because the ratio of conquest:alerts is still highly favorable, although the AIP will still be accelerating things somewhat.
Longwinded response done, short response:
1). It will definitely work as intended. However, if you start locking down territory as part of your shard hunting, and then stop at the outpost, the four frigates won't really compensate. They're very helpful, but on an entirely different scale than the firepower you'll get from a city hub. Don't make my mistake of taking territory on a city hub scale, getting to the outpost, then not getting to a city hub for a few hours while busy stomping out fires from say hybrid hives in a Grav Drill/Black Hole or Spec Forces Captain/Turtle-type AIs, while a Human Colony Rebellion or Zenith Miners get soak up a huge chunk of your time. Things may take longer than expected if you have a tendency to multi-task and a bad habit of forgetting to pause agressively.
2). I find that with the changes in the beta patches, the time and effort spent neutering should both be worthwhile, as long as you do it efficiently, before patrols become a force to reckon with. For the Spireling AI types I'm currently playing against, that means more Plasma Siege and Heavy Bombers. Here's how I'd guess I'd handle a Zenith Descendant system: send in fighters first, clear the guardians. Pull back, refresh my stock of fighters. All that agro'd fleet should gather on the wormhole, this is good. Send in my Fighters, Bombers, Frigates, AND importantly Riot Starships (lasers, shield, shotgun/tractor), make sure the fighters hit first. The Riot Starships will make chasing down kiting Zenith Bombards dramatically easier. As you won't have nearly as many valid targets for bomber starships, I might unlock the Zenith Starship line. They'll be particularly useful against Mirrors, Viral Shredders, Paralyzers, Chameleons, Reprocessors, Auto-Bombs (maybe), in addition to fighters and the like, while being able to pitch in to decent effect against the large number of medium hull-type guardians such as zombies and vampires. They'll also help against the Viral Swarmer a bit, but I often do hit and runs on viral clusters. Alternatively, I may be trying to Leech some Bombards or Electric Bombers of my own.
3). If you're aiming to consolidate your lines, yes, it would be best to take on the mark IVs earlier than later, by popping the command stations. You're going to need plenty of cleared systems for Spire hubs, anyways. If you have some sort of auto AIP (including spire civilians), then you can also handle these systems by agroing them, and throwing a lightning warhead in after they cluster around the wormhole. I'd only do this if it likely saved me a half-hour, and since my current game I'm trying out epic with spire civs and a Spire Hammer AI, these time saving measures might be key.
Under most circumstances, I recommend just sending in the fighters first to clear key guardians, so you clear the way for (if you're using them) Heavy Bomber Starships, Raid Starships, that will be detaching from your main force to clear distant outposts quickly. These types aren't especially defensive, so you shouldn't have to face too many Force Fields, Fortresses, or Eyes. Detachments of MarkI bombers/raid starships should prove quite capable of clearing out missile outposts and ion cannons while your main fleet is tied up in a heated fight at the wormhole, letting you wrap up the operation that much quicker, while the fighters are considerably cheaper and quicker to replace than your frigates and bombers. The Riot Starships should reduce a lot of the attrition from Zenith Bombards whether you just rely on the engine damage to reduce pursuit or use tractors to drag them back into the middle of a turret farm. Taking out those weaker distant outposts or guardians with can be a big help in keeping you from getting swamped at the wormhole by Zombie Guardians or chasing after fresh Zenith Bombards you can barely outpace in hostile territory when they have the opportunity to kite from the maximum of their range.
Once you have enough spire frigates or implosion artillery, you can even take out the wormhole guardposts, but initially I recommend just ignoring them.
