I call BS that its due to "illegal" immigrants. Undocumented immigrants mostly work in agriculture, the restaurant industry, or taking care of american households. The few blue-collar jobs that undocumented immigrants do take are the low hanging fruit that require little to no education or skill. If americans expected to forever be able to support their families on these types of jobs, then some people really need to step up their game.
These people are no longer competitive because they failed to innovate. They're priced out because their own government is and has been unwilling to do anything to help the non-wealthy and alleviate the level of income inequality.
Your first sentence is a bit of an oxymoron. Allow me to explain.
Without resorting to identity fraud, its nearly impossible for undocumented immigrants to find work because most employers require a social security number for payroll purposes. Even though they use a fake identity, they still get a paycheck, they still pay payroll taxes and pay into Medicare and Social Security. However, they get none of the benefits. Undocumented immigrants have no other choice but to commit identity fraud. Unfortunately for them, its a necessary evil. Their intent is not to dodge taxes.
I'm not saying all undocumented immigrants pay taxes but most are not opposed to it. A little google search will bring up plenty of research into this topic.
To your point about them breaking housing laws, all I can say is that its true but this isn't something that is limited to undocumented immigrants. Just take a look at the hacker houses in the bay. Maybe what is needed is more affordable housing.
I see where you're coming from but blaming undocumented immigrants for lowering the quality of life is a disservice. The US benefits immensely from undocumented immigrants but its something few want to admit.
These people are no longer competitive because they failed to innovate. They're priced out because their own government is and has been unwilling to do anything to help the non-wealthy and alleviate the level of income inequality.