The problem with Fynn was he really had no purpose, none whatsoever. If Days was promising a role on Days to those contest promoters, they should have had something definite in mind. But he came on...no story, no real connection to anyone, no involvement. So he was a doctor...heck, could have been any one of the ones who are background and have occasional lines. We see them all the time at the hospital.
No one needed a particular operation or treatment in which he perhaps could have been a specialist. heck, he could easily have been the bartender to the club and had more interaction with Salemites.
I do give the show credit for keeping him on, trying to find a place for him (am thinking that because they killed off Daniel, they needed at least one other doc at the hospital who was master of all things. ) But, to me, it just has not worked out.