It costs the Federal Government about $17,000 to round up and deport an illegal. Paying them $1,000 is cheaper in return. Maybe paying them even a little more, so long as we know they are leaving, is a cheaper way to get them to go. Right now, rounding them up in red states should be easier, then concentrate on the sanctuary cities with all their resources they can muster.
Many do want to come here legally, but getting a Visa or Passport from their own countries takes a year or two. So, if they are out of work, money, etc, they just try to walk across the border to find work. The US has offered Mexico to computerize their birth records and their criminal records to make getting a passport easier. They refused, probably because they are ran by cartels who use humans to smuggle drugs, and children across the border. Children for grooming to be prostitutes for pedophiles in America, some in high places in government and industry. Drugs to keep people dependent on the government to keep voting Democrat, etc.
Not all illegals are gang members, mules, etc. Some actually want to work, but Mexico and other countries have to computerize their records so we can screen out the bad apples. Visas should also be temporary with time limits.