I know that Rust provides some additional compile-time checks because of its stricter type system, but it doesn't come for free - it's harder to learn and arguably to read
Statically typed does not imply compiled. You can interpret a statically typed language, for instance. And not every compiled language is all that static.
For example, C is statically typed, but also has the ability to play pointer typecasting trickery. So how much can the compiler ever guarantee anything, really? It can't, and we've seen the result is brittle artifacts from C.
Rust is statically-typed and it has all kinds of restrictions on what you can do with those types. You can't just pointer cast one thing to another in Rust, that's going to be rejected by the compiler outright. So Rust code has to meet a higher bar of "static" than most languages that call themselves "static".
Type casting is just one way Rust does this, other ways have been mentioned. They all add up and the result is Rust artifacts are safter and more secure.
You can't safely do this yourself. That is, you couldn't write safe Rust which performs this operation for two arbitrary things. But Rust of course does do this, actually quite a lot, because if we're careful it's entirely safe.
That famous Quake 3 Arena "Fast inverse square root" which involves type puns? You can just write that in safe Rust and it'll work fine. You shouldn't - on any even vaguely modern hardware the CPU can do this operation faster anyway - but if you insist it's trivial to write it, just slower.
Why can you do that? Well, on all the hardware you'd realistically run Rust on the 32-bit integer types and the 32-bit floating types are the exact same size (duh), same bit order and so on. The CPU does not actually give a shit whether this 32-bit aligned and 32-bit sized value "is" an integer or a floating point number, so "transforming" f32 to u32 or u32 to f32 emits zero CPU instructions, exactly like the rather hairier looking C. So all the Rust standard library has to do is promise that this is OK which on every supported Rust platform it is. If some day they adopted some wheezing 1980s CPU where that can't work they'd have to write custom code for that platform, but so would John Carmack under the same conditions.
The thesis of Rust is that in aggregate, everyone can't be careful, therefore allowing anyone to do it (by default) is entirely unsafe.
Of course you can do unsafe things in Rust, but relegating that work to the room at the back of the video store labeled "adults only" has the effect of raising code quality for everyone. It turns out if you put up some hoops to jump through before you can access the footguns, people who shouldn't be wielding them don't, and average code quality goes up.
Well, the compiler is guaranteed that no mistakes will happen. It's the programmer who looses his guarantees in this case.