It happens more in the NBA and Euro soccer leagues I think. Don't really hear it much in baseball but I'm sure some ML star players ask for trades. Halladay I recall probably asked for a trade in 2009 and after the season when AA took over, but it was a given the Jays weren't contending and were going to move him with only one season left under contract. If the Jays didn't trade Doc, he probably would have been disgruntled but would have still worked extremely hard since he would be pitching for a contract. A star player in the middle of their contract and years away from free agency probably would have a different attitude.
I don't think the Jays will have that issue at all following this season, even if they miss the Postseason.
The struggles in 2023 definitely should be blamed more on the players than the FO. Though the FO will still get some blame if this team misses the Postseason. Atkins and his team were the ones who put this roster together, so yes their player assessment was off, in this case 5 regulars of their starting 9, which is a lot. Springer is an aging and injury prone OF, Vlad regressed already offensively in 2022, Kirk was always out of shape and really only hit in May/June of 2022, Varsho did have some flaws offensively even before he was acquired and Jansen has always been fragile and streaky. Don't know what happened to Chapman after April, but tough to blame the FO on him for his struggles. Like you said, if 2 or 3 of those guys play up to expectation, the Jays are most likely in a better position.
Regardless, some serious questions and decisions will have to be made for next season regarding some core players on the roster, especially if they miss the Postseason.