> Do think it's possible to write a C compiler that checks for use after free, double free, buffer overflows, index out-of-bound issues, etc.?

No, due to the way the language semantics works.

There are static analyzers that do something like that, MISRA-C, High Integrity C, Frama-C, but you are literally using C with Ada semantics at that point, thus it is almost like another language.