I'm always a bit leary when pushing pistons back, but more so with old junk on pads that have obviously been worn way down. It's not the pads but the fact the pistons have been "out" so long.
If crap builds on those exposed pistons or they swell at all where it's constantly "mashing" the pad backer, it can get sticky once shoved all the way back in.
Plenty of pistons are extended out a lot right now all over the world. They work ok in their present position -- after all they only move ‐‐ what ‐- 10 thousandths? during normal braking. But once you shove them back in 1" or more you're reintroducing a portion of that piston to the seal area and caliper bore. It can make all the difference between a functioning caliper and a sticky caliper. But then sometimes OEM calipers from 1987 still work great....so ya never know.
ALSO, I recently had your situation on my '07 F150. I arrived at my destination and noticeably detected a faint hint of burning brakes. I walked around and determined it was definitely right front. I ordered everything to rebuild a caliper and a new hose, but it's now been months and the problem hasn't returned. I dunno? But for now I'm not going to fix what ain't broken. If I were retired or bored I'd be more proactive rather than reactive.