The timer encourages you to "spend" AIP on something nice. The auto forces you to throw it away
Good point on the psychology.
I looked more into how CPAs and Golem/spirecraft exos work. Both of them incorporate a notion of an alternative minimum AIP based on game time. In other words, the higher your AIP, the bigger the CPA... but if you gain AIP slowly, then CPAs get bigger anyway. Much like being below the floor, being below the alternative minimum AIP represents a sort of AIP discount, where increasing AIP isn't going to make the next CPA bigger or make the next Golem-prompted Exo charge any faster.
Unfortunately that alternative minimum isn't obvious, so it doesn't have any psychological effects.
Exos & CPA destroying your entire fleet + defenses will take hours to rebuild
What's prompting these exos, and what's in your fleet that it's taking hours to rebuild? I'm assuming Fallen Spire...? I checked the wiki and unless that's been changed, Fallen Spire exos don't take AIP into account at all. The more cities you have, the faster they charge. Every exo is larger up to a cap based on the number of cities. Ergo, I'm a bit skeptical that this 'bursty AIP management to avoid stalemate' thing is really an issue with AIP.
If they're golem-prompted exos, then I am surprised that you have long refleets where you can't make offensive progress, because you have golems.
Also, you mentioned getting stalemated for long periods as a new player; ideally, very new players would not be facing any exos. If you're facing exos, you asked for it.
I wished that regular waves weren't just things for the newbies to be wary of.
The reinforcement => waves mechanic can make for pretty dangerous waves at high AIP; I remember Peter Ebersen reporting that this mechanic was more than doubling his wave size at one point. I was eating 8k waves by the end of my last game, at somewhere between 230 and 300 AIP, on diff 9. That was enough to keep me on my toes.
Note that in FS games, every spire city you build reduces that mechanic by 20%, until it doesn't happen at all once you have five cities. If you're playing FS, you're not getting the full brunt of this mechanic, and since that mechanic replaced the old 'effective AIP' cap for reinforcements, you're eventually facing uncapped reinforcements.
So if you're bored by regular waves, try doing the control-120-planets challenge without doing FS. Should get exciting in short order.
References:
http://arcengames.com/mediawiki/index.php?title=AI_War:Cross_Planet_Attackhttps://arcengames.com/mediawiki/index.php?title=AI_War:How_Exogalactic_Strikeforces_Work