The line for immigrating to the US starts in Mexico. You don't break our laws by entering illegally, commiting ID theft, tax evasion, etc. and then apply for citizenship.
I did say that was for those who had entered the US legally and did not know what it would mean for an illegal. Note too that you have to have a moral character and be law abiding. So taking that in mind, wouldn’t there need to be special considerations for illegals?