The H1B visa is explicitly designed for high skill (high paying) jobs which companies have (supposedly) demonstrated they cannot find enough citizen workers.

There are much simpler mechanisms to making that would make the enforcement mechanism more effective without destroying the economy, like prioritizing them by salary instead of randomly.

You could also just have a more proactive government which punishes businesses for abusing the visa category.

"Immigrants taking good jobs" isn't an immigrant problem, it's a big-business problem

>There are much simpler mechanisms to making that would make the enforcement mechanism more effective without destroying the economy, like prioritizing them by salary instead of randomly.

The Trump admin already did that too:

https://www.uscis.gov/newsroom/news-releases/dhs-changes-pro...