You are leaving a lot out here, the reason illegals get to keep most of their money is they do not have to pay for the things most Americans have to pay for- many do not pay taxes, many do not pay for insurance, do not pay hospital bills, use social services to get extra things they cannot afford on their low wages, do not have to pay for their children's education, in many states children of illegals get free tuition at State Colleges. If my husband and I would not have had to pay all those things I am sure we would have gotten further ahead also.
Things may be very different where you are, but I know many people here (even though we are on the border) do not hire illegals and manage to find decent help and somehow get by. Including jobs on farms, ranches, and in construction- even services like cleaning and waiting tables. Of course there are those who hire illegals and won't hire US Citizens, they usually pay low wages, and don't want to hear about unsafe work conditions or what have you. I find it hard to believe so many Americans are as sorry as you say where you are.
Don't forget people who are doing something illegal, like hiring illegal workers, will often attempt to justify what they are doing so they don't feel guilty. I know the employers here who do hire illegals say the same things you do- somehow other businesses make hiring Americans and following the law work out for them.
As far as hospital bills... those are the ones that have families. Usually the ones on work sites are covered by worker's comp or liability insurance.
The real problem is exactly what you brought up... paying their fair share. Now do these guys pay taxes?... I don't know. Do their employers "withhold" taxes?.... maybe..maybe not.
That's important, why? you ask...cause if they're "employees" they count as pretax expenses...that's if they're claimed and taxes legitimately withheld. Now follow this....what if the employers, the IRS and Social Security get money that is "withheld" but never "refunded" or "paid back". Then everybody makes money off the "illegal" and if he gets sacked or sent packing back to Mexico...that's even better. He'll never collect the money withheld, he won't get Social Security or Medicare he contributed to...and the employer still writes his salary off as a "business" expense on that side of the ledger depending on how much he/she claims to have paid the illegal.
Kewl, huh?
Follow the money. If Social Security is the greatest Ponzi scheme in American History...(it is) then how is the government going to "keep it going" for the next 20 years..... add more suckers to the bottom of the pyramid.... guess who those suckers are...., yep. "Illegal aliens".
of course that's only my opinion....and I could be wrong.