You are assuming that most of the languages people use don't have safe automatic memory management, right? This is of course incorrect. Now, lets compare Rust and Go, what makes Rust programs have fewer bugs, than Go programs? Is there any supporting research that shows how Rust eliminates any particular class of high level bugs? No, there isn't. So, no, Rust doesn't focus on eliminating bugs.
I'll make one effort in good faith to answer your questions, though I expect you're not interested in hearing the answer.
There is a class of programs where manual control over memory layout is important. For example, if you're writing an OS, as Mozilla is, you need this control to talk to hardware. It is also important in some domains where performance is important (e.g. games and big data.) Rust is the only language (outside of research) that offers control over memory layout while also providing memory safety. That is, no access to uninitialized memory, etc. This clearly eliminates a huge class of bugs relative to C/C++, the only language with substantial usage in this space.
Race conditions (data races) are considered important enough by the Go developers that they have a tool to detect them: http://blog.golang.org/race-detector In Rust these error cannot happen as programs containing data races cannot compile.
Then there is the usual modern type system stuff of eliminating nulls and so on.
I don't like arguments like that, as they don't have any supporting data. I happen to analyze significant amount of bugs in a large C codebase and things you are talking about don't seem to be as important, as you claim. But well, this is what's wrong with programming languages, nobody cares enough to do some research. That's ok though, we just think about languages differently.
I didn't say that memory safety is not important. I was talking about the need to control memory layout and other bells and whistles.
Anyway, you suggested Rust under false assumptions. Rust doesn't care about reliability and security any more, than most of the modern languages. Even Perl with its taint mode is more secure, than Rust.
Safe concurrency and memory management doesn't lead to reduced bugs? Eliminating unsafe memory access doesn't lead to increased security?