You are correct, the fact that some group of molecules has much smaller moment of inertia than the rest does not make the group except from the equipartition theorem.
But there is a physical reason for why sometimes certain regions of phase space or degrees of freedom are discarded as non-contributing to total energy. In other words, there is a reason for why equipartition theorem or equal treatment of all degrees of freedom is not accurate.
This reason is "extremely slow equilibration". Some degrees of freedom are in only a very weak interaction with the rest of the system. For example, collisions of spheres do transfer energy from translational to rotational energy, but only very slowly. If the system achieved temperature by quickly accepting energy from outside, some rotational degrees of freedom may not have enough time to acquire the same temperature as the other degrees of freedom. The more smooth the spheres, the longer the time to equilibrate. If this time is astronomical, for some regions of phase space it makes sense to just exclude them from calculations, because the probability they are realized is extremely small so they do not contribute much.
Another similar example: atmospheric gas in a closed vessel with microscopic hole in the wall through which gas molecules escaping to vacuum with only a slow rate. Because of the hole, the phase space available is infinite, and the equilibrium state is that density is close to zero everywhere. But because the hole is so small, the gas in the vessel achieves temporary quasi equilibrium with itself, with some high temperature and high density. To find properties of the gas, only volume of the vessel is important, not the vast space outside it. Again, a part of the phase space is discarded because it is not relevant in the time period considered.
There are other examples: such as oxygen and hydrogen gases in a cold vessel forming water after a long time, or escape of atmosphere molecules from Earth's gravity field. These processes are so slow they are usually ignored.