Not that it would eliminate security exploits caused by logical bugs, but most those exploits were already taken care of with Burroughs Algol variant (1961), Modula-2 (1978), Cedar (1981), Ada (1983), .... but oh well.
Those are due to programmer error. The fact that C doesn't lie to you means that it takes a bit more experience to program properly; as with all things, with great power comes great responsibility. You don't blame the gun for killing people, you blame the person for shooting it.
Not even the very best C programmers will write memory safe code. When you write C you will write exploitable code, no matter who you are. Don't blame the programmer for stepping onto a mine in the minefield, blame the minefield.
http://www.cvedetails.com/vulnerability-list/year-2016/month...