I completely agree with everything you point out. The argument I am bringing up is not about implementation, it's about "if they didn't use C, they would have less (security) problems": No.
C is the way it is towards secure coding because there are compromises to satisfy other dimensions. <Fancy new language that promises to solve all of C's problems> is either making huge sacrifices in these other dimensions or is at best an experiment.
We understand C's weak points so well (due to being widespread, battle tested, really simple, or what have you), that most of the time it's safer (read: more secure) to tread dangerous well-understood territories carefully than uncharted ones only promising to be safe.
I'm only superficially familiar with Rust, but my understanding was that it was basically "C with strong memory guarantees". I naively thought that its entire purpose was to avoid such trade-offs.
It's a bit more upfront work to satisfy the compiler but I've found the payoff in debugging memory issues to be completely worth it.
This is a false choice. Go and Rust are not replacements for each other. They both have qualities which make each better suited for different environments.
Rust is actually capable of replacing all uses of C, Go's runtime will generally be an impediment to using it in certain cases.
Also I would argue that there are entire classes of bugs that are still available in Go that are not in Rust, that make it less suited for security. Null pointer exceptions, and unchecked errors are the two that come to mind.
I know it says "partial" implementation, but it's quite good even so, and has had everything I need. It doesn't do SSLv2, but nowadays that's more virtue than vice.
Erlang has an independent SSL implementation as well; it binds to OpenSSL but as I understand it just uses the heavy-duty math parts, not the protocol parts, which are instead written in Erlang.
Non-C SSL implementations in memory-safe languages exist.
Note that "but are they as well road-tested" or similar such things would be moving the goal posts. Not necessarily wrong or bad objections, but different objections. Probably nothing, not even the other C implementations, is as well "road tested" as OpenSSL, but, then again, OpenSSL hasn't exactly passed that road testing with flying colors now, has it?