So nurses, professors, teachers and artists will be in higher demand and they'll have to pay them a better salary to fill positions? which may attract people who currently avoid those career cause they lead to poverty? Yup I'm sold.

And as others said, add a cost factor to train an citizen for every H-1B issued. Actually, slap a 350% tax on all the salaries paid to H-1Bs except for the first 15 people (or, I don't know, 3% of the overall staff, whichever is higher) and make sure it's hard to game with shell companies, body shops and subsidiaries.

Precisely 0% chance it'll happen in the current administration, and it's anyone guess if there will be administrations after this one, but a few hours of additional thinking around this solution (this is the first 3 minutes roughly) could make it work way better. Remove limits, make it really expensive, give some rights to the people who come on it, use the money to address real shortages, and watch companies stop abusing it.

P.S. European here, with 0 interest in coming to work in the US.

I had no idea there was a huge shortage of professors, teachers, and artists.

If they’re not willing to pay up, then there isn’t really a shortage.

If we think those things have positive externalities (such that we want them to happen even if they wouldn't win an auction) we should subsidize them.

Nurses generally can't get an H-1B, and professors are exempt. Your argument makes no sense.