2. New QB is brought in, but Mac Jones "wins" a QB competition
One of the benefits of keeping Mac Jones around even if a new QB is brought in is that Jones has experience with the team and much of the personnel on offense. Even though he's largely been awful, the familiarity with the offense might be seen as an advantage if a new regime were to be brought in. Furthermore, what if the Patriots don't select a QB in the first-round of the 2024 NFL Draft? Depending on how the board falls, that's a possibility.
Taking a QB in the second or third round would likely be working with a developmental prospect who might not be able to start day one. Well, in that case, there'd be a pretty good chance that Mac Jones could again earn the starting job for the New England Patriots. Another advantage here is Jones being out there potentially taking his lumps with a new offense and new players, and keeping the other QB out of harm's way.
If the Patriots had a new coaching staff, the team would likely take a little while before they got comfortable with what the coaching staff wants to do. This would also mean some inconsistencies on offense, and if you're the new staff, wouldn't you rather have Mac Jones out there instead of a hypothetical rookie QB? Jones would likely have to deal with up an down OL play and some rough terrain, all while the rookie QB absorbs the new offense.
It'd almost be like the new staff would use Jones sort of as a decoy or test-dummy until the unit found their footing, paying the way for the rookie QB to eventually take over.