For example, in garbage collected languages the programmer does not need to think about memory management all the time, and therefore they can think more about security issues. Rust's typesystem, on the other hand, can really get in the way and make code more opaque and more difficult to understand. And this can be problematic even if Rust solves every security bug in the class of (for instance) buffer overflows.
If you want secure, better use a suitable GC'ed language. If you want fast and reasonably secure, then you could use Rust.
"Don't use Rust because it is GC'd" is a take that I think basically nobody working on memory safety (either as a platform concern or as a general software engineering concern) would agree with.
I don't disagree with the premise of your post, which is that time spent on X takes away from time spent on security. I'll just say that I have not had the experience, as a professional rust engineer for a few years now, that Rust slows me down at all compared to GC'd languages. Not even a little.
In fact, I regret not choosing Rust for more of our product, because the productivity benefits are massive. Our rust code is radically more stable, better instrumented, better tested, easier to work with, etc.
If your program loses track of which file handles are open, which database transactions are committed, which network sockets are connected, GC does not help you at all for those resources, when you are low on heap the system automatically looks for some garbage to get rid of, but when you are low on network sockets, the best it could try is hope that cleaning up garbage disconnects some of them for you.
Rust's lifetime tracking doesn't care why we are tracking the lifetime of each object. Maybe it just uses heap memory, but maybe it's a database transaction or a network socket. Either way though, at lifetime expiry it gets dropped, and that's where the resource gets cleaned up.
There are objects where that isn't good enough, but the vast majority of cases, and far more than under a GC, are solved by Rust's Drop trait.
Not disagreeing, just mentioning.
The brilliant thing about RAAI style resource management is that library authors can define what happens at the end of an object's lifetime and the Rust compiler enforces the use of lifetimes.
Concurrent Pascal or Singularity also fit the bill, with actual operating systems being written in it.
There isn't even specific language support necessary, it's on the library level.