Some algorithms require mutation to have a decent time complexity and ST allows you to implement those.

There is a tiny cost for each mutable memory location since the garbage collector has to work around then. A single array won't even be measurable, though.

Also, there are some referentially transparent algorithms that can't be implemented via ST - like laziness.

Direct mutations for a mutating algorithm is certainly faster than rebuilding a data structure representing a set of variables. Most of the time. Though, there are exceptions where they're equivalent thanks to GHC's optimizations (e.g. splitting up a record's fields into n registers).

This might help answer your first question: https://medium.com/@jonathangfischoff/are-mutable-references...