But... why the latter?
The multi-variable case is trickier, especially because (result, err) is such a common pattern and you neither want to impede the very common case of storing a result into a new variable nor to require a profusion of differently-named variables for errors that are very likely to just get folded anyway. So it allows it if any of the variables are new rather than requiring all. But clearing a large chunk of the bug surface is still much better than not.
(This is only my extrapolated reasoning, of course.)