-AT decay only has an impact if you dont go to war enough - not to mention that with only one military idea, you have plenty of spare mil power to reroll generals all day...even in my non-westernized tabarestan>persia game I had enough spare MP to reroll generals while staying eye to eye with the AI in miltech. once you have reached the point where manpower is no longer an issue, AT is at 100 all the time anyways.
AT being high after a war is useless, what you really need is AT before a war when you are making generals. Having AT decay slower after a war is therefore a good thing. Even 10 or 15 AT brings substantial benefits. Manpower is never no longer an issue.
I think you are overestimating the influence of combat ability - discipline trumps combat ability, and when you reach the point where you have those two idea groups done, you should have no need for the combat ability to win battles (unless for some strange reason you'd take quality as first military idea, and that'd just be you own fault then

). moreover, once you are at miltech 18 and beyond, infantry devolves more and more into a meatshield for your cannons.
Combat ability is effectively half as good as discipline, so +20% combat ability is worth +10% discipline for just your infantry.
I think you misunderstand the combat system in some way. Cannons at miltech 18 deal 2.4 fire + 0.25 shock base damage * .5 for being in back row = 1.35 damage, while infantry deal 1.1 + 1.15 = 2.25 damage. Infantry are therefore by far the main damage dealers at that time. It's very, very late in the game that cannons actually surpass infantry. In total +20% combat ability to infantry is worth about +7.5% discipline overall.
You always need better soldiers. Everyone runs out of manpower sooner or later, better soldiers ensure you run out of manpower later.
As TMIT already pointed out, vassal feeding and coring are not mutually exclusive, doing both is the best way to go.
You can always make more vassals to consume more land. The best way to go is to make more vassals and get a better idea group. Anyone that thinks you need to mass-core in the brave new world of AoW really needs to take a game to play with vassals. The only time you need to core something is to get around the "no vassal full annexation of 2/3PMs" rule, and you have more than enough ADM to do that yourself without needing coring bonuses.
the cheaper merc bonus I find very notable in early game where mercs rule, but even if you disagree there its still plain better than the one from innovative
Mercs are at +150% maintenance, so -33% only takes you from 250%->217%, for an effective savings of 14%.
Quantity, meanwhile, gives a savings of 19%(.9*.9 = .81 to maintain) to BOTH normal units (including your expensive cannons) and mercs. Nonwithstanding the fact that everything else in quantity is great.
+goods produced is more powerful than you give it credit, especially since AoW where a lot of previously mediocre trade goods can become quite valuable, for example cloth or iron. of course any money-making idea gets obsolete after some point, but it might still be relevant if you take the group early.
The only instance I would consider it significantly valuable is if you were a CN or a native american doing a lot of colonizing, since it's far more powerful on lots of small BT provinces and especially since it ignores autonomy. For most nations in Eurasia its not really a big benefit, the majority of other idea groups will translate into a greater economic benefit. At least it's better than the Mercs discount though.
All this said, I'm not saying Admin is a bad idea if you're a super-blob in SP bent on WC with nothing in your way other than coring time. I can't fathom why people want to play such a game though, but if they do then go ahead and take admin. I totally understand why it would be super useful given the circumstances.