At a broad view, we get to a place where there's no "bug" when "what happens on overflow" is what the program(mer) wants.
All I said is that you can remove undefined behavior from signed overflow without having to introduce checks to every arithmetic operation and without having to specify any particular behavior or outcome. The technical term for this is "unspecified behavior" and the consequence of making overflow unspecified behavior is that the consequences of overflow, while still unspecified, must be bounded in space and time, unlike undefined behavior whose consequences are not required to be bounded in either space or time.
You can define a behaviour today that they'll all get, but you can't define a behaviour that matches what each programmer needed when they wrote their operation. Some of them can wrap safely. Some of them would need to saturate. Others would need it to abort.
The problem isn't that the behaviour is undefined per se, it's that you can't tell afterwards which potential behaviour the programmer needs, and choosing one behaviour e.g. wrap will break everyone who actually needed saturating, or trapping, etc.