Because it makes them look like they care for the people who elected them ("the imigrants make crimes/are taking jobs" narative). In reality the politicians only care about the biggest bider.

In some states it is, but state-level elected officials have only weak levers with which to influence the rate of illegal immigration.

I don't know much about the topic, but conservative commentator Ann Coulter complained that although he certain got votes by talking about it, Trump didn't do much against illegal immigration and probably doesn't really want to do much about it.