Having used sanitizers to find a couple C++ bugs I am convinced that Rust is a better solution to that problem. I would never have found the C++ issues without extra tooling, so just use Rust, learn the rules and let the compiler make you write correct code. To clarify, yes ASAN is awesome but using a language where you don't need it is better.
When there's no more C++ there will be no bugs in the C++ code base ;-)
j/k, though I've fixed memory bugs, overflow, use after free, etc. written by people much smarter than me. without static analyzers, valgrind, and afl its possible that some would still exist nearly a decade later.
I'm not sure what you mean by "all the analysis"; by default Rust just calls malloc.
It's true that a C++ custom allocator will have lots of "unsafe" code, but this is really where C++ shines. The tooling is more complete, the aliasing rules are better documented and understood, the language fights you less, the stdlib has explicit support, it is easier to control the codegen. Rust cannot bring its strengths to bear on this sort of problem.
