[momoschili]

Simply speaking, "l" describes the number of nodes. In the same sense that a particle in a box with sin(nx) wave function has more nodes the higher energy (or momentum) state it is in.

As for why l==0 has no rotation going on at all, one would say that this should be expected. Qualitatively, the symmetric sphere does not change with rotation, so how would we tell if it is rotating or not? And perhaps the next step is controversial, but if there is no way to tell, maybe there is no dependence? This is a similar argument to why the electric field of an infinite plane is constant with respect to distance from it.