Yes. I don't think Linux would have succeeded if written in a language other than C. Today is a different story.
Yes it matters to me as an end user if my web browser is more or less likely to have vulnerabilities in it. Choice of programming language has an impact on that. It doesn't have to be Rust, I'd use a browser written in Pony.
If I were making something that had to be low-level and not have security bugs, my statement would be:
> I’m not smart enough to build a big multi-threaded project in a manual memory-managed language that doesn't have vulnerabilities. I want help from the language & compiler.
The size and longevity of the team matters a lot too. The larger it gets the more problematic it is to keep the bugs out.