A1S is the only savage floor where no TP regen makes sense regardless of kill speed. So much down time.
I can't imagine not using any TP regen in A2S. Even in a 6 minute kill I would expect to play roughly 30s of Paeon. On my A2S that are over 2k I played Paeon twice for 8:14 kill and 3 times for both 9:14 and 9:34 kills. 7 minute kills with my previous static static also used Paeon twice. All the logs are available, but I'm not sure if they're okay to post here.
In A3S you will need Paeon for kills over 10 minutes provided everyone is pressing buttons. Your group may even need a little in add phase depending on party comp, and if they were maximizing aoe potential for Equal Concentration. I often end phase 2 with almost zero TP. But that's mainly if I know I will get a Goad sometime before final phase. For slower groups I plan on a few ticks of TP before add phase and roughly 30s going into the first embolus phase. That's enough for a lot of groups, but in the case that it isn't then perhaps a 3rd short Paeon close to the end. A3S depends a lot on group comp and player gear/skill. Even without aoe for Equal Concentration I can end add phase with almost 0 TP due to getting so many extra GCDs because of low party DPS on the adds.
A4S will also require TP regen. Different strats can change the timing of those regens as whether or not you kill certain dolls can dictate whether what times you'll have MP for regen. In my previous group we killed every doll so things were different. But now I've adjusted to groups only killing both dolls on 4th leg. Typically I'll do a few ticks going into leg 2 if the MP is there. Maybe a tick into leg 3 then foe. Maybe 1/5 a bar of MP for Paeon going into leg 4. Paeon between the two leg 4 add sets. In final phase I honestly don't remember, but I would expect to Paeon at least once in final phase. Maybe after first pentacles (especially if sac'ing).
As always, it'll depend on party comp and kill times, but you will have unhappy physical DPS/tanks on every floor except for A1S if you do not provide TP regen.