"To my mind, what's wrong is the idea of stopping these people who just want to work. Why not set up a system that allows people to cross the border more freely if there's work for them in the U.S.?"

Ah, then they would have to be paid a proper 'legal' wage, whereas if they are 'already illegal' then those crminal (already rich and powerful from these activities) thugs who love to sponge off the weak and disadvantaged can get a clear run...