The second half of the sentence doesn't follow from the first. Take everyone's favorite example, signed integer overflow: all you have to do to avoid UB on signed integer overflow is check for overflow before doing the operation (and C23 finally adds features to do that for you).
Taking a step back, the fundamental thing about UB is that it is very nearly always a bug in your code (and this includes especially integer overflow!). Even if you gave well-defined semantics to UB, the semantics you'd give would very rarely make the program not buggy. Complaining that we can't prove programs free of UB is tantamount to complaining that we can't prove programs free of bugs.
It actually turns out that UB is actually extremely helpful for tools that try to help programmers find bugs in their code. Since UB is automatically a bug, any tool that finds UB knows that it found a bug; if you give it well-defined semantics instead, it's a lot trickier to assert that it's a bug. In a real-world example, the infamous buffer overflow vulnerability Heartbleed stymied most (all?) static analyzers for the simple reason that, due to how OpenSSL did memory management, it wasn't actually undefined behavior by C's definition. Unsigned integer overflow also falls into this bucket--it's very hard to distinguish between intentional cases of unsigned integer overflow (e.g., hashing algorithms) from unintentional cases (e.g., calculating buffer sizes).