No, just because entities are in a cartel doesn't mean that they all wield equal power within that cartel. Risk avoidance is big, but it's not the only thing operating.
And it's not a single century-old ruling: there are narrower exemptions that allow the other sports to function in very similar ways, and also for collectively-bargained labor contracts, which add up to virtually the same result. But as above, MLB can't really help the judicial exemption being challenged: they can't stop people from suing them, and sometimes those people refuse to be paid off.
Standing to challenge and refusing to be paid off (plus resources to pursue it) is a very small (maybe nonexistent) group
