Job changes are very dangerous for H1-Bs in other ways and employers know it (and abuse it, nearly all of them). Basically if your employer finds out you're looking for a job and you don't already have another job lined up, they can fire you out of spite, and you'll have to GTFO the US within (IIRC) 2 weeks. There's absolutely no recourse. Even if you are in a protected class, you're very unlikely to sue unless you're in the US and have lots of money (which H1-Bs typically don't). So few people bother unless the situation is really dire.
It's not just H1-B either. F1-OPT gets abused in a similar fashion.