A competent C/C++ programmer will have a lot less of problems like buffer overflows and crap like that, I don't think a buffer overflow has been found in any code I've written during my 10 years as a C programmer.
I have still written code that has security issues though, most of them stem from poorly designed code and are not necessarily a language problem.
I'm not claiming to be a super human here, I've had my fair share of gotchas, like off by one errors and issues with pointer arithmetic when refactoring code and so on and we might actually reduce the time needed to verify that C code is safe if we change to another "safer" language, but I'm 100 % sure that you still have the issue with poorly designed code even with a "safe" language. And from my experience it's a lot harder to find those problems, since you need to understand how the code base works and how it fits together to find those issues.