I would agree with you that the establishment clause also tied the hand of state governments except it was specifically written to do the exact opposite. To keep the federal government from establishing a national religion and from interfering with the state established religions which were explicitly allowed.
But had it not been written that way, then the states should not be allowed a trojan horse exception to a federal restriction.
But had it not been written that way, then the states should not be allowed a trojan horse exception to a federal restriction.