Simple solution: Unlimited visas for people being paid $125,000 or more (adjust for inflation over time), and people on such visas pay 2% extra income tax. That

Simple solution: Unlimited visas for people being paid $125,000 or more (adjust for inflation over time), and people on such visas pay 2% extra income tax. That 2% goes to funding whatever department is looking into visa fraud. Companies that are trying to fill low-wage jobs won't have access to these visas. Companies attempting to abuse the system have a well-funded group of people trying to find them and stop them. There's also an incentive for people with such visas to work hard to try to get a green card, and eventually become citizens, to get rid of the 2% tax hike.