10 is more than three times 3.
I'd also say that if most (really?) regions have no knights, it's probably more to do with the fact that noble:region ratios everywhere are pretty low. Check out these regions without knights: most of them will have vacant estates anyone could pick up.
That’s the problem. Anyone can pick them up, but they don’t because there’s no incentive, and the lords are quite content not having knights. Actually it’s
better not having any because all they do is cut into your tax revenue until they get their own region. It’s not a coincidence that the most stable realms typically average around 1 – 1.5 nobles per region.