>If someone is here long enough to obtain a state id, there's no reason to detain them on suspicion of their status having expired

It seems like you believe that if somebody had been long enough in a state to obtain a state id then their status in the country is legal forever. In the few states where I've got id it took about a month to get an id - you need to lease some housing and get two bills. But even if it took 50 years to get a state id it would not change anything - a state id is not a proof of legal status in the country. Immigration officers can detain people on reasonable suspicion, which is the same standard that is needed for a traffic stop.