Doesn't it also mean that any non-trivial migration (e.g. which requires data transformation or which needs to be structured to minimize locking) has to be defined elsewhere, thus leaving you with two different sources for migrations, plus some (ad-hoc) means to coordinate the two?

(I would say that it is conceptually perverse for a client of a system to have authority over it. Specifically, for a database client to define its schema.)