Most(?) browser vulnerabilities are caused by errors in C++ code which would not be exploitable in memory safe languages. One of the goals of Mozilla's Servo is to write a browser that's memory safe without compromising performance.
My point was that it's not a C specific problem, though. Most browsers are in fact built on C, I agree. This is due primarily to the speed and performance of the language that is harder to reach with other languages.
It is definitely a more difficult language to write, as it is much more "raw," but that doesn't make it inherently unsafe to use, or any more unsafe than other languages.
If you vote because you think C is unsafe, carry on. You're wrong, though.