>C is not impossible to secure
Expert compiler writers and computer scientists disagree with this assertion. History seems to be on their side.
Writing "secure" C requires meticulous attention to detail at every level, intimate knowledge of undefined behavior _and_ of compiler optimization, along with the exact options passed to the compiler. It requires comprehensive reasoning about signed integer behavior and massive amounts of boilerplate to check for potential overflow. It also requires extensive data-flow analysis to prove the provenance of all values (as Heartbleed taught us) because a single mistake in calculating a length leads to memory corruption.
To put it another way: No one can write fully secure C code. It has never been done to date. All non-trivial programs written in C contain exploitable security vulnerabilities. The combinatorial explosion of complexity makes it impossible both to formally verify and to permit human reasoning about the global behavior for all likely inputs, let alone unlikely ones.
I'd say OpenSSH (since SSH2) has a better track record than most webapps, as unfair a comparison as that is. In terms of local robustness, there's SeL4, which is also a bit unfair (since it took about a decade for a team of geniuses to prove enough properties to make it probably not very buggy).
I don't disagree with your use of OpenSSH as an example.
You might argue either way, but a straightforward C program can be correct if it is well formulated, but a straightforward web app can not be correct unless it is fully mitigated.