This is false. Under US antitrust law, /monopolistic behavior/ (that is, behavior that tends to create monopolies), e.g. predatory pricing and very large mergers, is what's generally regulated. It's not actually illegal to be a monopoly per se, and you don't have to be a monopoly to fall afoul of antitrust law.
"Assuming that the estimates are correct, got aways have fallen significantly since 2006. In that year, Border Patrol estimated over 600,000 aliens successfully crossed the border and evaded USBP. By 2011, that number had evened out to just under 100,000, where it has remained until today."
https://cis.org/Huennekens/Enforcement-Estimates-DHS
Plus hardliners are very much disputing that some refugees are fleeing from real danger.