The biggest problem for JPA providers seems to be that records do not have a default constructor.

The opposite is true: the problem is that JPA requires default constructors (as you realize below).

If JPA providers could add some flexibility in how objects are instantiated/initialized, records could easily be supported. Supporting initialization through non-default constructors could also be beneficial for Object-Oriented Design: entities could have a single constructor and fields could be made final (JPA could even infer that @Column.updatable = false for final fields).

That's a slightly misguided perception. Why should a final field not be updatable? Immutability, on the object level, doesn't mean read-only column in the database. It's perfectly valid to want to stick with an immutable domain model, create new instances using "wither" methods, and persist those to fresh instances as updates to a row in the database.