In 1991 there were already five or so. Plus other 'cheap' Unixes like Xenix and the usual big names.
If Linux didn't happen we'd have a few thousand BSD variants by now.
The great thing about Linus was the combination of technical brilliance and his forceful personality.
The original BSD that Bell Labs gave to Berkeley in 1974 was anything but open source. It was an operating system that Bell had provided to the university with source code available for modification and redistribution ONLY to other universities WHO ALSO HELD research licenses from Bell Labs.
And it still wasn't open-source in the early 90's when Berkeley scrubbed all the proprietary bits out of it and tried to sell it for profit. That's when AT&T sued them.
So even if you HAD a copy of the BSD source code pre-1994 it wouldn't have been the same as someone handing you code and asking for your advice on it. You would have certainly found yourself in court if you modified early BSD for redistribution.
Bell Labs was allowed to finally start charging for UNIX after the split was done, so they went after the most attractive fish that were getting paid to sell UNIX, as AT&T wanted to bring it all back in house.