> For example, if I use a language that doesn't allow buffer overflows to happen, I've eliminated an entire class of security bugs being caused by programmer error.
There are several assumptions behind "if I use a language that doesn't allow buffer overflows to happen" which you aren't taking into account. For instance, are you entirely sure that the implementation of that language's compiler will not allow buffer overflows to happen? We have a good example of a possible failure of that model in Heartbleed: when it came up, a bunch of people in the OpenBSD community raised their eyebrows, thinking hmm, that shouldn't happen for us, we have mitigation techniques for that. Turns out -- for performance reasons -- OpenSSL was implementing its own wrappers over native malloc() and free(), doing some caching of its own. This, in turn, rendered OpenBSD's own prevention mechanisms (e.g. overwriting malloc()-ed areas before using them) useless. The language specifications may not allow such behaviour, but that doesn't mean the implementation won't, too.
You're also underestimating a programmer's ability to shoot himself in the foot. Since I already mentioned OpenBSD and Heartbleed, here's a good example of a Heartbleed-like bug in Rust: http://www.tedunangst.com/flak/post/heartbleed-in-rust . The sad truth is that most vulnerabilities like this one don't stem from accidental mistakes that languages could have prevented; they stem from fundamental misunderstanding of the mode of operation which are otherwise safe constructs in their respective languages.
Granted, this isn't a buffer overflow, which, in a language that doesn't allow arbitrary writes, would be an incorrect construct and would barf at runtime, if not at compile time; but then my remark about bugs above still stands (and I'm not talking out of my ass, I've seen buggy code produced by an Ada compiler allowing this to happen), buffer overflows can be increasingly well mitigated with ASLR, and the increased complexity in the language runtime is, in and by itself, an increased attack surface.
Edit: just to be clear, I do think writing software in a language like Go or Rust would do away with the most trivial security issues (like blatant buffer overflows) -- and that is, in itself, a gain. However, those are also the kind of security issues that are typically resolved within months of the first release. Most of the crap that shows up five, ten, fifteen years after the first release is in perfectly innocent-looking code, which the compiler could infer to be a mistake only if it "knew" what the programmer actually wanted to achieve.