What is an example of a use case where relying on the current behavior would be a good thing?
For an exception to happen, one has to force more than what was already forced when the handle was closed. The vast majority of instances of this---as far as I can tell---are people immediately closing handles they've lazily read from, and an exception is probably more informative than the empty input they currently get.
For correct-given-the-current-spec code to break, it seems like it would have to be relying on one part of the code forcing the input before closing to be an implicit signal to another part of the code that inspects the input after the closing. But I don't see a reason to encourage/support that kind of design.
I'm in favor of this change, in case that wasn't obvious. :)