Well sure, that is what we would do if we actually wanted to reduce illegal immigration. However, that would deprive businesses of their supply of cheap, disposable exploitable labor. Illegal immigrants are going to take whatever wages they can get, as long as they are better than what they can get in Mexico or whatever other country they came from. They are not likely to complain about wage and hour or safety violations, and they can be laid off without having to pay unemployment compensation.
IMO, the real goal of many ostensibly anti-immigrant people is to maintain the status quo. That is why they support mostly ineffective stuff like walls or other "border security" measures, and push propaganda to keep anger directed at the immigrants themselves, rather than the people employing them. They don't really want to stop illegal immigration. Neither do they want to see illegal immigrants granted legal residency or citizenship, as legal residents or citizens would likely be less inclined to put up with bad treatment.
