What uv does is parallelize the final download of packages after resolution, and batch pre-fetch metadata during resolution. I don't think these benefit from async, due to their batch nature classic multi-threaded download pools are probably the better solution, but I could be wrong!
Experiments have been done on the former in pip and didn't find much/any improvement in CPython, this may change in free threaded CPython. For the latter we currently don't have the information from the resolver to extract a range of possible metadata versions we could pre-range, I am working on this but it requires new APIs in packaging (the Python library) and changes to the resolver, and again we will need to benchmark to see if adding pre-fetching actually improves things.