POPCNT is an interesting example. Runtime dispatch (with a conditional branch) would actually make sense for it because it's comparatively difficult to implement from scratch. PDEP and PEXT might be similar (but I don't think compilers pattern-match for it, unlike POPCNT). AArch64 uses localized run-time dispatch extensively because LL/SC atomics are so very bad on current cores, but there isn't anything comparable in the x86-64 space (POPCNT isn't that frequent).

For many other things, like using a YMM register to copy a 32-byte struct or a variable shift, run-time dispatch just not make sense. You will only see a benefit if you generate this code unconditionally. For FMA, you wouldn't even get bit-identical output, leading to testing concerns.