I think it is a matter of choice of audience. If you want pure functional languages, there are plenty that will rock your boat (Haskell, OCaml ...).
But, to my mind, I see Rust as a somewhat "modernised" C/C++ with, like Python, the most interesting and accessible parts of FP backed in. It is a balance and it is fragile. So, as I said, I hope that Rust will keep that fine line.
All that said, it only is my opinion, I might be wrong and the wider audience might be ready for "harder" FP. But I doubt it.
The influence of "FP" on rust is really more like the influence of Haskell's type system. Rust is pretty far from a functional language but it does share a lot of type system features with Haskell: type classes, sum and product types, HM type inference
With C++, I can't say the same is true. Some libraries try to alleviate that, of course.
Making things compact and focused helps. Of mixed-approach languages, I see Kotlin's approach to integrating FP as more successful.