I wondered about this too. I think I resolved it in my mind by seeing the game as granting every piece one degree of freedom that goes from discrete to continuous: for most of the pieces, it's distance from the origin, since they move in straight lines. But knights are already more constrained than that anyway, so for knights, the continuous DoF is axial instead.

This also makes sense when you put any given piece in the middle of an empty board and plot all of its potential moves— for every piece but the knight, "joining up" their possible landing sites gives continuous distances from the starting point, but if you join up a knight's landing sites, you get a circle of r=√5.

So in short, I agree with the OP's decision on how to handle knights.