Unless you are a permanent resident hopeful what you say is correct. For a lengthy period of green card process does not allow portability of the GC application. I can hardly imagine anyone who has H1B but not has a GC application in the process or about to make that application. At that point visa and the GC application becomes a golden handcuff. If shit hit the fan you are politely reminded of this. It did for me when I was caught in the middle of a power struggle in the company and asked of my loyalty. Employers are not stupid to remind you this (productivity tanks), generally it goes very silent, but if they have to they will remind you, don't worry about that eventuality.
Very true, but the way I see it is that I've been given ~4 years to find the 'right' position for me. Now that I have done that, I am happy to be "handcuffed" in order to get a green card, because I know my company isn't a ridiculous parody of The Office.
