Without Hash::Util::FieldHash, no reference to the filehandle is kept anywhere (since the hash would only keep a stringified version), so there's nothing preventing it from being destroyed. But it does make sense to stop tracking a filehandle if it can't be accessed anywhere because the variables holding are all out of scope.
I think returning the filehandle is a good idea, although it can be used for cleanup, it should only be a temporary solution until the real issue with the code is fixed. And if someone trying to fix their code just keeps collecting references to their handles without releasing them, the problem probably is not with your module in the first place. Maybe you can keep a weakened reference to the handle though, that way unless the user keeps a copy of that reference, you have access to the handle, without preventing its deletion.