On existing techniques - Type-Constrained Generation paper is discussed in the blog post (under Constrained Decoding), and I'd group typed holes in the same bucket.
The problem with those methods is that they're inference time: they don't update the weights. In this case, constrained decoding prevents the model from saying certain things, without changing what the model wants to say. This is especially problematic the more complex your type systems get, without even taking into account that type inference is for many of these undecidable.
Meaning, if I give you a starting string, in the presence of polymorphisms and lambdas you might not always be able to tell whether it completes to a term of a particular type.
On the syntactic difference: I'd gently reframe. The question isn't whether syntactically different programs are semantically equivalent, it's that regardless of which form you pick, the existing methods don't let the model learn the constructor choice.
That's what the next section is about.