LLMs do trip up when they generate Rust code, but they also do when generating any other language. The big difference is that the Rust compiler refuses to compile broken code faster, whereas Go will just let you SIGSEGV on edge cases without warning.
The recent TLA+ hype here on HN shows that Rust may just be the beginning here. There are valid, safe Rust programs that will crash, the language isn't perfect. The older languages with more math and validation behind them (Ada?) are probably even better suited for generated code, but they don't have the hype culture to capture mainstream attention (and even fewer people have the ability to really review that code).
There's an alternative solution of course: use platforms like JS/.NET/JVMs/Python to run code that cannot violently crash because of the language runtime around it. That comes with a performance overhead but it's good for prototyping without as many stability footguns and with faster compilations.