You miss the biggest issue. The cheap Mexican labor holds down wages of working class citizens.
Take new construction. Contractors are forced to hire illegals to be competitive with other builders who use illegals which drives citizens out of the workplace if they are unwilling to work at cheap Mexican wages.
This might hold down the cost of new construction but it also holds down the value of old construction, such as our homes.
When the builders are forced to use citizen labor it drives up the cost of the new construction but to the benefit of working class citizens and those whose homes are already built.
Another real problem that you didn't mention is that the immigrants will end up voting for Democrats in larger numbers than for Republicans. They become addicted to government hand outs as soon as they arrive and the Democrats constantly romance them with promises of free stuff. Republicans can't do that or they lose their meaning.