Great Question, but I don't think those who have issues with illegal migrants are interested on who benefits from the cheap labour they provide. They're more interested in violence against illegal migrants being the solution such as shooting them, etc, as they see them as a threat more than those who are bringing them here. If they were interested in a solution, they'd be taking their grievances with the politicians & the companies that hire illegal migrants, as protesting outside migrants hotels & burning migrants homes have not solved anything.
Some keep claiming that they've no issue with migrants who are here legally, but only illegal immigrants. We know that's not true as eastern Europe migrants were here legally & they were also hated as much & that resulted in Brexit. And this time I've a feeling the result will be digital IDs, which will still not yield the solution they seek.
I've not considered that, but it wouldn't surprise me, these people like to manipulate the public. In the times we live in, you should at least have non perishable food that can last more than 3 days.