Depends on the program, and it can be a very useful tool.

Rust has Mutex::get_mut(&mut self) which allows getting the inner &mut T without locking. Having a &mut Mutex<T> implies you can get &mut T without locks. Being able to treat Mutex<T> like any other value means you can use the whole suite of Rust's ownership tools to pass the value through your program.

Perhaps you temporarily move the Mutex into a shared data structure so it can be used on multiple threads, then take it back out later in a serial part of your program to get mutable access without locks. It's a lot easier to move Mutex<T> around than &mut Mutex<T> if you're going to then share it and un-share it.

Also It's impossible to construct a Mutex without moving at least once, as Rust doesn't guarantee return value optimization. All moves in Rust are treated as memcpy that 'destroy' the old value. There's no way to even assign 'let v = Mutex::new()' without a move so it's also a hard functional requirement.