Since many years, performance-critical libraries have used runtime/dynamic dispatch.
Our github.com/google/highway intrinsics even automate this. You can write your code once and it is compiled for each instruction set, and the best codepath is selected at runtime.
The other major problem I have with dynamic dispatch, at least for the SIMD code I've written, is that you have to do so at a fairly high level of granularity. Most optimized routines are doing as much fusion & cache tiling as possible and so the dispatch has to happen at the level of the higher-level function rather than the more array-op-like components within it. And mostly, that means you've written your (often quite complicated) procedure several times uniquely instead of simply accelerating components within it.
I have not used Highway - if it dramatically simplifies the above, that's excellent!
I agree dispatch should be at a reasonably high level. This hasn't been a problem in my experience, we have been able to inline together most SIMD code and dispatch infrequently.