As an H1B, while there is employer tie in at some level, I am free to change jobs. What I am not free to do is to stop working. That fear certainly does indirectly result in lesser job mobility.

For example, opportunities like say going to Recurse Center, or having the freedom to have a decently long sabbatical etc. even with a 6 month emergency fund are not available. The other thing is no freedom to pursue any other job, i.e working on a startup idea during the evenings or weekend, or writing a technical book etc. for money is not allowed.

There are certainly issues with the H1b system, i.e. the lottery, low salary cap, multiple applications per person to game the system etc, but employer stickiness is not one of them, at least for people who are qualified.

The major problem is due to long wait for green card for people from China, and almost impossible wait for people from India. My friends who were not born in these two countries have been able to get a green card within about a year, after getting an H1B, while I am looking at a more than 20-30 year wait.