Earlier quoted context omitted.
Only if the end-user is the one compiling the software, on the same very system they'll be running it on. Which is true of GPU shader kernels, due to how GPU drivers work; but isn't generally true of CPU object code (unless you're on Gentoo.) What you'd actually want is a matrix of variant implementations burned into the binary, with runtime (or process-boot-time) hardware detection that swaps symbols out to point to…
If you want the library to perform that selection, you also need the "correct" / most efficient implementation to be independent of your workload. I'm not that familiar with SIMD performance characteristics, but I wouldn't be surprised if that's not always the case.
If that's the case, then the selection logic would be trivial: figure out the full hierarchical ID of the uarch you're running on, then search for the longest prefix match in the table of available impls.
If things work more like you're imagining, though, then I suppose the process-boot impl-selector would narrow down the impl matrix to just the subset that are legal on the running uarch; pick one arbitrarily to be active at first; and then wrap the calls in a handler that gradually re-works the called function in a way reminiscent of a profile-guided JIT, but without the need to actually synthesize any code at runtime — instead, it'd just be a multi-armed bandit passing-through-to and re-ranking competitor impls, with decreasing sampling of the non-first-ranked impls as confidence-in-score-separation increases.