What Holly says is exactly right. Arbitrary type information not back-propagating and side-propagating between statements is an intentional aspect of the function builder design. One of the reasons we didn't put function builders through evolution last fall was specifically that the implementation could have propagated types that way, which we didn't consider acceptable or sustainable for the feature to commit to.
Part of our thinking here is that we've been conscious of the possibility of type-checking all closures in their surrounding context the same way that function-builder closures are. That would eliminate the problem where multi-statement closures passed to generic functions often need to declare their signature. But to consider that, we need to (1) make sure that the type-checking model isn't vastly different from what it's been before and (2) stave off as many sources of exponential complexity as we can. That means restricting how types propagate between statements to be as consistent as possible with a statement-by-statement model.