And Miri is very popular in Rust. Even if a Rust project doesn't have unsafe, sometimes people still run Miri with it, since dependencies might have messed up their unsafe usage.
And every instance of unsafe that I could find (except one, in test-only code) was a call to libc with a clarifying comment on why this particular use was safe. That is, all (or at least, all of it that I could find) was wrapping an unsafe API with documented (and usually straightforward and local) invariants that maintain safety, such that the calling code is safe.
I'd say that the fact that miri's trophy-shelf[0] has 39 entries and is 7 years old and still regularly updated is a pretty good indicator that memory bugs are sufficiently rare in rust so as to be notable. That is the opposite of "regular"
The vast majority of Rust code out there doesn't use the `unsafe` keyword at all, and the vastly smaller amount of unsafe code that exists allows for focused and precise testing and verification. You really have no idea what you're talking about if you're trying to say that Rust is anywhere in the ballpark of C or C++ here.