I've been thinking for a while that a lot of the problems (wage suppression, non-existant shortages, etc.) of the H-1B visa program could be solved by replacing

I've been thinking for a while that a lot of the problems (wage suppression, non-existant shortages, etc.) of the H-1B visa program could be solved by replacing the lottery with a market. Instead of companies applying and randomly getting visas, start from the highest-paid salary and accept down the list until hitting the cap. Companies dealing with legitimate shortages can pay for the certainty of filling their gaps, and American workers are happy because the program becomes a mechanism to raise wages. As with all things in economics there's probably some third-order effect that will have us scavenging the ruins of civilization for canned food, but I'm curious to hear what would be.