A bit obsolete perhaps, but not too old since USB 3 seems to be a pain for many: I finally managed to delete old drivers properly. Then, SURPRISE SURPRISE Windows told me, at restart, "drivers were installed successfully". In my case it was some VIA stuff...
I believe it was one of the latest Windows Updates that did it. So, just to inform you, anyone having problems with USB 3 might do well by getting rid of any non-functional drivers, and get important or recommended updates.
None of the advice I got or found on a dozen sites helped. It was a dead end. I still thank you all.