No, but as seen in the first chunk of rust code added, the amount of logic that needs to be constant-time is a) very, very limited to a few primitives only b) algebraic in nature (put differently, it's not where memory bugs will pop up, so using rust over C doesn't even buy you much).
For instance, ASN.1 parsing doesn't need to done in constant time in the vast majority of cases (and in all cases I am aware of).
> And then when said logic stops being opt-in, why wouldn't the same problem arise?
Some friction will certainly remains, but it will be nothing compared to the current breakage.