While C was intended to run as close to bare metal as possible, and 99% of current implementations do, that doesn't have to be the case. The C specification describes an abstract machine, and uses abstract concepts, with explicit "as-if" rules saying that implementations may, in many cases, do whatever they want, providing that conforming code runs as if it would on a naive implementation.
So there's no reason at all that, for example, pointers have to be implemented as actual bare addresses in a virtual address space which cannot be bounds checked. It should be perfectly possible to create a new implementation, with a new ABI, which defines pointers as a checked type such that all accesses through a pointer are accurately bounds checked, with a guaranteed "virtual" segfault happening whenever an invalid read or write would have occurred.
Sure, it's not ABI-compatible (by defualt) with current bare-metal C ABIs, and would require shims to work with bare-metal C libraries - but that's no different than Rust and similar other new languages. Sure, it's not quite as fast as bare-metal C implementations due to enforced bounds checking, but it's not going to be slower than Rust and similar which do the same job.
And the advantage would be, we wouldn't need to rewrite all our code. We could just recompile all the existing C code we already have to this new safe ABI, rather than having to rewrite everything from scratch in some new language!
Sure, C isn't the nicest language to use. But we already have plenty of existing code that uses it. Why don't we just write a new compiler back-end and take advantage of all that code in a safe manner?