The idea that people will just shift to other kinds is ludicrous. There isn't a fixed quota of bugs per developer-hour. In my personal experience, Rust code absolutely has fewer bugs than most other languages.
Several large surveys have found that approximately 70% of bugs in C and C++ projects are memory safety issues.
I will say that I have written a fair amount of Rust, and never had a bug in a sub-100-line Rust program, which is a huge difference compared to C.
For more complex things, arguing with the borrow checker has often led me to weird solutions that seem to work, but are unlikely to be 100% bug-free.
I would also like to point out that the surveys are looking at known bugs, and memory safety bugs are now very easy to find, thanks to the large number of memory safety analyzers that exist.
The analyzers exist because memory safety problems are significant, but the fact that they are 70% of known bugs does not imply that Rust code will have 30% of the bugs that you would find in a C equivalent. In my experience, if the C equivalent is short, Rust code usually has 0% of the bugs! If the C equivalent is long and complex, it could be a lot higher.
Several large surveys have found that approximately 70% of bugs in C and C++ projects are memory safety issues.