The only reason the jobs are low paying is because there's a large number of illegals willing to do them. In other words an artificial and undesirable increase in available labor. Remove the illegals and the wages will go up.
Round them up and kick them out.
And with them, prices.
You are exactly right.
Most of these illegals come here and leave their family back in Mexico where the cost of raising and providing for a family is much cheaper.
A bunch of them will pool their money and live in a trailer or an apartment and split the cost. That's why they can work so much cheaper.
They also don't have to pay income tax, social security tax, or state income tax, or property taxes, or house insurance, or auto-insurance, or buy car tags, medical insurance, etc: that the American citizen has taken out of his check, or has to pay trying to provide for his family that's living here.
Six or seven American dollars will by a lot more necessities in Mexico than they will in Dallas, LA or New York.