The congress shall have power … to arrange national party meetings … — and to make all party laws which shall be necessary and proper for carrying into execution the foregoing powers, and all other powers vested by this constitution in the republican Constitution party government, or in any department or officer thereof.

This intrusion on state party sovereignty doesn’t follow from the Constitution, but is needed in the party constitution to keep more-Progressive states from running open contests, primaries, or non-proportional voting that would select less-pure national candidates, damaging brand purity.