A couple of things:
If the Tigers are as bad as many seem to expect them to finish, why would one assume that another team would rush to hire him? Do guys who have multiple losing seasons in a row land cake gigs often?
This organization appears to have given him a lot of say / leeway in personnel decisions since he has arrived, more than most organizations give their manager, particularly in this day and age.. why would he give that up to go into a situation where he may not have that same role?
Along with the second point, that additional say allows Hinch the opportunity to help build something, which is the kind of thing that could further his legacy, particularly given that he sort of inherited an ascending team in Houston and had his reputation tarnished by the sign stealing scandal while manager there.
I think AJ knew what he was getting into when he signed up for this role and just haven't seen any evidence that he's not invested in the success of this ballclub.