So, in order to win, you need to kill both AI command stations. But when you kill one, are you actually killing that player--or is it "okay, our team has two, and we can both keep using the other one"?
Specifically... Does killing one AI home station prevent that player from reinforcing? From sending waves? Obviously it doesn't make them stop caring if you kill their other planets--that would be insane--but is there any actual utility that you gain from killing off one station that could be taken advantage of? I noticed that the flavor text on the home planet intergalactic wormholes says they keep letting ships in until both homeworlds are dead, so right now my assumption is that killing one player actually doesn't do anything useful at all.
I can see a few strategies where wiping out one planet in midgame could be useful, without committing to finishing the game on the spot, even if there's no actual game effects from doing it (aside from 'you don't have to do it later'), but this question is more about the actual game effects that happen when one AI player dies.
Bonus question: Is there ever a reason NOT to nuke the second AI homeworld, either right up front or after you trigger their reserves? I just used a nuke for the first time last game, and was delighted to discover that yes, if you cut off supply from the enemy homeworld, their fortress (and maybe ion cannons) are permanently disabled. That's a HUGE game changer, since I normally can't get that fortress out of the way until after I kill the station. An extra +50 AIP when my fleet is sitting on their doorstep doesn't sound very big, especially when it almost certainly makes the difference between needing two waves or three to kill the bad guys. It seems most effective after I've triggered their reserves, since those are mark <5 units and therefore quite vulnerable to the nuke. Even if I don't nuke, an EMP to shut down the ion cannons seems really obvious. I'm only playing on difficulty 7.0 and 7.3 for now, but still...it seems like nuking will be an integral part of every endgame for me, unless there's a good reason not to.