It probably needs to be made easier then, so the H1B can switch jobs as easily as a native worker.

I have not had to deal with US immigration, but my impression is the H1B process is between the employer and the government. It would probably help to make that between the employee and the government, to give the employee more control.

I used to work at a company that had a lot of H-1Bs and treated them terribly. Whenever someone was trying to transfer of get a green card there was some involvement with their current employer, and I always used to wonder "What incentive to they have to do this quickly and correctly?"

The other problem is that AFAIK the 10-year-long Green Card clock resets if they change jobs, so there's a strong incentive not to leave.

H.R.392 - Fairness for High-Skilled Immigrants Act of 2017 [1] aims to fix the green card backlogs by removing the per-country quotas.

[1]: https://www.congress.gov/bill/115th-congress/house-bill/392/...