So, this might be coincidence, but it might also be worth checking out. After reading this thread today and starting to think about it again, I managed to duplicate the starting energy loss on a fully warmed up pitcher three times in a row using the "Schedule to pitch" option. Granted, my test is an early-inning situation and may not occur the same way in a real game situation (let alone Season/Franchise), but it's still the only kind of consistency I've seen in this occurrence. I'll lay out exactly what I did so others can duplicate it and see if they get the same results:
For this test I have the "Warm-Up pitchers" option turned off (I explained what it does above, and it really has no bearing a test like this). In a play now game using the Cubs, I fast-forwarded the top half of the first inning. Then, before the first pitch of the bottom half I went to put Pedro Strop in the bullpen using the regular "warm up" option. After the first out, I went back to the bullpen and activated the "Schedule To Put In Game" option (Strop is often around 15-30% on the bar by this point). Then I play out the rest of the inning as normal, and before the next inning starts I accept the prompt to bring in Strop (now fully ready because of the half-inning break). Each time (again, 3 games/attempts in a row), he came in with less than full stamina - I wouldn't call it 3/4 but maybe 85% of his bar and 50% or less confidence as opposed to the ~60% a pitcher usually enters with. It's essentially the same look a pitcher gets when you bring him in completely cold.
Here's the kicker. I also tried this same test
without using the schedule option, just bringing in Strop as a normal move the same number of times. The energy/confidence loss didn't happen once.
Knowing why this is happening is the first step to us avoiding it and, potentially, the devs fixing it. So if you're interested, give this a try and see if it's the same for you. Somehow I doubt it's this simple as this is a thing that has been around for years. But it would make a lot of sense if it's been around for as long as the "schedule" option has.