The biggest misunderstanding people have around UB is—in my experience—the (often) subconscious assumption that UB optimization is around optimizing the performance of code that exhibits UB. It is not.

You're partially correct. foo() won't have any access to y so won't be able to modify it… unless foo() is written in way that exploits undefined behavior. Compilers can (and should) assume that foo() is not written pathologically in a way that writes into the frames of functions higher in the call stack, and so can make the above optimization.