What you are describing exists: ASan. We have a pretty good answer to the question "is ASan sufficient to prevent memory safety problems in practice": "no, not really".
> Rust, BTW, doesn't entirely guarantee memory-safety, either, when any unproven unsafe code is used, and even when it isn't (e.g., have you proven LLVM's correctness?). We always make some compromises on soundness; the question is where the sweet-spots are.
Empirically, Rust's approach has resulted in far fewer memory safety problems than previous approaches like smart pointers and ASan, with only garbage collectors (and restrictive languages with no allocation at all) having similar success in practice. Notice that the working approaches have something important in common: a strong system that, given certain assumptions, guarantees the lack of memory safety problems. Even though those assumptions are never quite satisfied in practice, empirically having those theoretical guarantees seems important. It separates systems that drastically reduce safety problems, such as Rust and GC languages, from those that do so less well, such as ASan and smart pointers. This is why I'm so skeptical of just piling on more mitigations: they're helpful, but we've been piling on mitigations for decades and UAF (for instance) is still a big a problem as ever.