str -> [u8] is free from a performance perspective. It is internally equivalent to a type cast.
[u8] -> str requires a UTF-8 validity check, but is otherwise also internally equivalent to a type cast (i.e., no allocations). I assume this is what Armin meant by "almost" free.
FWIW, I do think that "internally and externally UTF-8" is the best approach to take. If Rust's string type used, say, a sequence of 32-bit codepoints instead, then lots of lower level string handling implementations would be quite a bit slower than their UTF-8 counterparts. (For at least a few reasons that I can think of.) UTF-8 also happens to be quite practical from a performance perspective because it lets you reuse highly optimized routines like memchr in lots of places.
In any case, the abstraction is not lost completely. Rust's string types provide higher level methods without needing to know the encoding used by strings. e.g., You can iterate over codepoints, search, split and so on. The abstraction is intentionally leaky. e.g., You are permitted to take a substring using byte offsets, and if those byte offsets fall in the middle of a UTF-8 encoded codepoint, then you get a panic (or None, depending on the API you use). You are indeed prevented from doing some things, e.g., indexing a string at a particular position because it doesn't make a lot of semantic sense for a Unicode string.
You might call this a "failure" because it leaks its internal representation, but to me, it's actually a resounding success. Refraining from leaking its internal representation in a way that is zero cost would be absolutely disastrous from a performance perspective when implementing things like regex engines or other lower level text primitives.