I have a bunch of six groove Douglas 308 barrels. They shoot fine.
I have a couple of Krieger four groove barrels, .223 and 308, they shoot fine.
I have shot out a couple of .223 Wilson six groove barrels. They shot fine.
I have one Wilson six groove on a 30-06, it shoots fine.
US military barrels, the Krag, M1903 were all four groove. The M1903A3 had four groove and two groove.
The two groove barrels shoot cast bullets better than the four groove.
These old military barrels are not that good compared to today's barrels. We have better barrels today.
Having even number of grooves may keep the cutters in line when rifling a barrel. So that is probably why so many barrels have even number of grooves.
I do not know why barrel makers started using six groove barrels. In old NRA reprints, I think the thought was more grooves meant less bullet distortion. I do not know of 8, 10, groove barrels. I think microgroove barrels were 12 groove.
The quality of the barrel and the quality of the chambering job are far more important to accuracy than the number or type of grooves.