The road to Hell is paved with good intentions. Your plans to get out quick may run into economic epicycles and then your clever plan ain’t so clever.
The most insidious thing they did was delay the green card application as much as they could, and just drag things out on purpose. Since I am Albanian/European, I could get it faster as my country is not on the per country cap that Indian and Chinese applicants are. They knew it, as they kept dragging out the first stages of the applications on everything. It was mental abuse.
By 2011, the economy was recovering, and I did switch, but I had to redo all the green card application stuff again.
The employee should just be able to do the process themselves, and handle it the papers with their own lawyer.
It is clear that the H1B is setup to maximize the benefits to large corps, and not necessary the american economy/people.