> The cost of this borrow checker is huge: every reference in every program needs to be annotation with whether it's shared or mutable

No. You need to "annotate" a mutable binding since bindings are immutable by default. But that also means that immutable bindings (ie the vast majority) does not to be "annotated". And even when you do need to, you literally just add the keyword `mut` as in `let mut foo = 42;`.

> and you often need to splatter confusing lifetime annotations all over the place. It adds a big learning curve to the language.

Again an extreme exaggeration. There are a few cases here and there where you need lifetime annotations, but most often the compiler simply infers them for you, allowing you to elide them completely. Specifically, you only need to do it yourself when it's ambiguous from which input(s) the output is derived.