I'm not precious about a player wanting to "come and play for the badge". Next to no player joins a club for that reason. Yaya Toure wasn't sure about joining City. He becomes their best players ever along with De Bruyne. Tonali wasn't sure about leaving Milan. But the money Newcastle offered them was too good. He's now one of their most important players (after an interrupted start obviously).
Ultimately, before you even try and sign a player, you should do the work in finding out if their a good enough character, that they'll get to work for whichever club they do end up signing for. If you hear good things in that regard, then don't worry about it.. if you think there could be problems, then you shouldn't go for them anyway
I'd rather have a top talent that you need to pitch the club to over a middling talent that dreams of playing for us.. Because the latter would also need convincing if other clubs were actually bothered to be interested in them.