There are probably many such vulnerabilities in this giant code base, being exploited by those who have resources to find them.

If OpenSSL is written in Rust, to what extent will the vulnerabilities be reduced (assuming that Rust is supported by the host, of course)?

rustls can serve as an alternative.[1] Dirkjan Ochtman, one of the main contributors, wrote about it in this thread.[2]

[1] https://github.com/rustls/rustls

[2] https://news.ycombinator.com/item?id=33423296