I disagree here. Player can also join based on the manager. If the player thinks the manager is very good and can get the best out of you in the manager's system then it makes sense why the player will buy into the project, thus choosing United over the others' big shots. For example: the player might think, wait if I joins City under Pep and he plays 433 means I will be playing in the similar role of how I plays at Barcelona, which clearly not working for me, but if I joins United, Ten Hag knows how to get the best out of him and I believe Ten Hag is destined for success and we had great time in 18/19.
And also another example, look at James Rodriguez was willing to join Everton because of Ancelotti. James wouldn't join Everton if Ancelotti wasn't there, and he would choose different club.