Smells like the Pats wanted the personality off the roster to me, not necessarily the player.
Saw tweets from Mike Reiss and Breer both suggesting the reason NE wanted to make the move was QB room dynamics, making the QB room more conducive for Maye's growth. How Milton contributed to making it less conducive or the dynamics worse no one said but feel like it's likely pretty close to what you are saying here.
Maybe that explains NE's angle. Why he could not get back much more in a trade who knows but he did end up drawing back a similar return to what Fields ended up netting the Bears.
I reviewed this earlier in this thread and in the NE team thread.
It's been said that Milton considered himself an NFL starting QB all along, going back to when he was drafted. Apparently, after his performance against the Bills to close the season, he or his agent (or both) started suggesting internally to the NE brass that Milton wanted a fair shake at starting this year and wanted an open QB competition. Maye is a made man in NE, and there's no way they were going to let Milton (or anyone else) try to compete for the starting job. That's where the unease and trepidation of Milton becoming a problem is said to have come from.
As far as his trade value, based on his age, his college tape, and his perception as a long-term developmental project, that all trumped what league talent evaluators viewed as a preseason game performance against the Bills. Essentially, his value from that one game didn't really move any. The teams that inquired apparently all offered NE similar Day 3 draft options and viewed him as a 25-year-old project. The Pats certainly did not get any offers tantamount to Milton being a future starter, and certainly nothing near the 2nd or 3rd round picks the Pats were reported to have been looking for.
I'm not really buying that the Pats "granted Milton his wish" of a trade to DAL, as he's in no position to start there either. The Cowboys are committed to Prescott for at least the next 2 years (moving on from him would be a massive cap charge). I'm also not really buying NE turned down a better offer. I view that as they had a better offer probably by a few slots in the draft from a rival AFC team that they didn't want to trade him to. But I don't think there was a big difference in the trade offers they received.