Complete cores: can be done during a war (though it's more costly).
Replenish manpower: can be done during a war by switching to mercenaries.
Integrate vassals: can be done during a war provided you start the integration before you start the war.
Wage war on the other front: that's assuming you have another front that is different in culture and/or religion than the one where you waged your last war.
Fabricate claims: can be done during a war, just not on your current target or its allies that honored the call.
Look for targets of opportunity: can be done during a war.
If you're not a role-player, there is no reason to ever be at peace unless you need to click the annex/integrate button - and it should be obvious that I'm not a role-player. I don't mind the concept of AE and coalitions, as I do believe the AI needs tools to defend itself, but I wish there was something I could do about it other than sitting around with my thumb up my ass. If there was ever a good reason to expand on the Espionage branch of diplomacy, this is it.
Now here's a decent reply. Iduakil please take notes and learn from this fine gentleman.
Now, to address it: That is all true, of course. With a few notes:
Coring progress is frozen when at war with someone with a core on the provinces you're coring. At the moment in my Commonwealth game coring time is 112 months for me, which is OUCH, but hey. Fair game.
I'm no longer in need of manpower as at this size as even at war with other powers in my european front my manpower barely takes a dent while sieging several provinces at once with stacks of 40+, and battles aren't even much of a thing, but at the beginnings I barely had enough manpower+cash for taking on my enemies, like Muscovy.
Vassalizing/annex: yeah, only pushing the button requires peace, that much is true. Scant little time at peacetime with a few allies though!
Well, if you're going to be conquering a lot, you might as well plan ahead, yes? Set up your fronts so that you can flip between them at will.
Fabricate claims: true, but can also be done during peacetime. With long borders you can fabricate on a lot of targets, and that takes diplomats and time! Always aim for having all the claims you can on possible war targets.
Scouting: yeah, can be, but would be distracting. When I wait for truces to end I look through disputed successions, others' wars, alliances (alliance with Uzbek was Crimea's downfall in my latest game as I could get at them without poking Otto).
There's ways of juggling AE, through region, alliances and improving relations (friendly folk seem to get a lot less AE than neutrals). Truth be told, if not for truces and AE/coalitions, at this point I could just steamroll the whole world, that would make the game quite trivial. I don't really fancy unending war myself, I like that in Pdox games you have these little mechanics limiting it, as opposed to, say, Total War games. Never touched a CA game after trying CK2 for the first time.