Yes. A green card auction would be great. Expand it to some large number and get rid of all the huge variety of visas and paths to citizenship. Maybe half or more of all immigration to the US could go this route.

After some years of high demand and high prices, I imagine that the price would drop to some stable level. When that happened, we might have an opportunity to bring some sanity to the illegal immigration problem in the US. In some more sane world, both parties might agree that a person that can prove they have been in the US for some number of years can pay for a green card at the auction rate (gov financing available).