Legally, you're required to pay taxes even if you're getting underpaid. Many undocumented people use ITINs. Your whole argument is based on false assumptions.

Gosh golly gee, someone who decided to break the law to enter wouldn't possibly break other laws for their own benefit, would they!?

I don't care if "many" people do anything: if they are here without status, they should be removed post haste.