At that point it is better to have some kind of DSL that should not be in the main language, because it would target a much lower level than a typical program. The best effort I've seen in this scene was Google's Highway [1] (not to be confused with HighwayHash) and I even once attempted to recreate it in Rust, but it is still a bit far from my ideal.
I agree about having a DSL. It may not need to be low level, you could have an array language like APL/J. But glsl would work for me too, the important thing is to lure developers to expose parallelism.
The kind of things you can use direct SIMD for is a reasonably-different space than array languages; while some things can translate reasonably, APL-likes get much less pretty on operations where elements don't have homogeneous meaning/mapping, e.g.: the base64 conversion of OP. (for reference, I work on https://github.com/dzaima/CBQN, an implementation of BQN, an APL derivative, and we have a DSL for implementing SIMD primitives for it (and sometimes scalar ones too): https://github.com/mlochbaum/Singeli)
[1] https://github.com/google/highway