Ten Hag must win the dressing room because everything starts from there. Some of Manchester United's senior players look selfish in the game and actually this should be resolved rather than bringing in lots of new players. I agree that there are certainly some players who come and go, but improving the performance of existing players must be the focus at this time.
I agree with your point, Manchester United already have a lot of talented players and adding more players when they can’t manage and deal with the current ones will make the existing feel unappreciated of that fact and assume the team don’t really value them for bringing in young players like them. The management might also want to make the team more competitive by bringing in rivals to those players that don’t perform well or are full of themselves. Whatever they do or intend to do, they should work on improving the overall performance of the team because they are lacking in all positions now which they need to address before it gets worse for them in the league.
I don't think there should be much concern about the feelings of players when new players get added to raise the competition. Every player playing on that level as a professional has to be able to cope with competition. This is not about individual wishes or feelings, it is about the team as a collective and competition is a major part of it. It is actually what makes everyone better. But the issue isn't competition, the issue is the lack of the ability to smoothly integrate players into the system (if there is any system). Manchester United had lots of great talents and couldn't get them to play well for the team. But this can have many reasons and the coach might be one of them.