Of course Schiano has baggage.
Personally, I believe he would have been fine at Tampa and got a shitty deal being run out of town the way he was. But that said, the general story on Schiano is that he is a stubborn control freak who had moderate success at Rutgers and went on to be an unmitigated disaster at Tampa Bay. Whether its fair or not, a lot of NFLers will never forgive him for trying to turn the kneel down over against the Giants. He has a MAJOR image issue form that and the things players said about him. This is why he did not get another head coach offer in the NFL, and did not get a head coaching offer from any Power 5 program this year, despite the fact everyone knew he was looking to get back into the coaching game. Its the reason his agent got SI do a huge puff piece on him showing how soft he was and how much he was trying to learn from his mistakes.
The proof is in the pudding. Schiano is working as an assistant to his friend, the best coach in college, for one reason ony - career rehabilitation.