Their response to having access to the military cut off was to simply militarize ICE into a paramilitary group with powers that are more broad than even the military would get for such enforcement. With the advantage that ICE can be staffed entirely with fascist friendly true believers while the military is mostly staffed with just regular humans.

If they deployed the military as police enforcers it would instantly become the most ethnically diverse and lowest paid police organization in the country. They have to have considered that.