Rather, I think that the static analysis we see in today's languages just isn't powerful/flexible enough to reason about safety in a lot of the patterns that we know are safe. I'm also uncertain if it can _ever_ catch up to what we know to be safe, but I wouldn't be surprised if we get there in a few hundred years.
For example, borrow checking is a step forward and can guarantee safety, but does nothing about the other half of correctness, specifically liveness. [0]
Linear types (like in Austral [1] and Vale's higher RAII [2]) can help guarantee liveness, but we still have further to go.
Both are based on single-ownership (in the C++ sense) like Rust, which introduces errors that e.g. Haskell would not.
But even Haskell (and LiquidHaskell which has linear types) don't go far enough; Coq goes even further.
So yes, like you say, we have a long way to go w.r.t. correctness, even past the borrow checker though it is a big step forward.
To my original point though, even all of these tools put together will put restrictions on a program such that it sometimes won't be allowed to take the most optimal approach. Perhaps someday we'll get there!
[0] https://en.wikipedia.org/wiki/Safety_and_liveness_properties