I'm not sure that it was actually quite this way. Let's look at what happened to Palmer after he scored as a sub in the CL away to Bruges in October 2021, his second-ever senior appearance for City. He made a further 8 appearances over the next 3 months, and totalled 348 minutes, before sustaining an injury in January that basically ended his season. Prior to that, Guardiola had commented publicly that the player would likely be given first-team minutes to allow him to develop.
The following season, it really didn't work out that way. Palmer stayed fit for basically the entire campaign and played 851 minutes across all competitions. But he had only two league starts, both in May 2023 after the title had been won, and one start in the CL, in a dead rubber against Sevilla in the final group stage fixture. It's a fairly pitiful haul, in fact, and hardly indicative of him being a player our management rated.
IMO the available evidence suggests that Palmer didn't leave because he was demanding game time. He left because, through the 2022/23 season, he was given the impression by Guardiola's continued team selections that the manager simply didn't regard him as a serious member of the senior squad. And it would have been easy to remedy that impression had Pep wished. I believe he could quite easily have given Palmer plenty more minutes without compromising results, but obviously didn't want to.
Now, I don't blame Pep for this. He picked the line-ups he saw as best for the job at hand and we won the treble. And when letting Palmer go, we got a big fee. Palmer got a move to a club that was prepared to back him and made his point. Everyone's a winner. But I think Palmer's stance was perfectly reasonable and I'd reject the implicit criticism of him that the above narrative engenders.