As I recall, I signed up for the beta, so maybe they removed this requirement after release. I deleted Brave, and I was pretty sure it was for this reason. I just re-downloaded it and installed it, and sure enough there was no log-in requirement.

Was there some other privacy-touting or "alternative" browser that came out in the last couple of years?

One thing I did find annoying after installing it just now is that it doesn't import bookmarks from Safari, but rather only Firefox. It would be nice if it did; in fact it would be cool if some browser would do bi-directional bookmark syncing with Safari, to piggyback on iCloud syncing across devices.