This is not true at all, there is a well-defined H1-B transfer process that I've used myself. Your new employer petitions USCIS for a transfer (similar to filing a new petition, but cheaper), and you can switch jobs once it's approved.

The problem for people in my position is there is no legally available downtime. If you get fired, or quit so you can search for a new job, you no longer have a right to remain in the US. There is no way to fix this without entirely redefining what the visa is supposed to be for: a particular employer being unable to find local employees to fill a position.