> IMO the problem is that H1B employees are stuck at the employer for the duration of their green card process, and so end up both paid lower and unable to escape abuse.

This is not true. Transferring your H1-B to another employer is entirely possible, the new employer will have to file the application as usual, but the application is not subject to the annual H1-B quotas.

At least this was the way it was several years ago. I doubt the process has changed since.