This caveat is the problem. You lose a ton of properties when you have “interior mutability” (I.e. an object typed as immutable is, in fact, mutable). You probably can’t appreciate the benefit if you haven’t actually used a purely immutable language. Rust touts “fearless concurrency”, but it’s nowhere close to what you can get with Haskell’s guarantee.

> not powerful enough to write safe programs that are as efficient as C programs (since you can't modify memory)

Wrong on both counts. The vast majority of mutable algorithms can be expressed recursively and immutably. Consider haskell’s Vector library. It generates C-equivalent output a lot of the time despite being immutable and much higher level.

The one exception I’ve run into is algorithms that inherently rely a lot on random array writes (like in-place random shuffles), and in this case Haskell has the ST monad for externally pure, referentially transparent mutability that cannot escape into the rest of your program. The fact that haskellers almost never need or want to use ST is very strong evidence that, in fact, you don’t really need mutable semantics at all once you’ve figured out what you’re doing with immutable data.