I think H1Bs should not even be required to hold a job at all. The offer they initially receive from the "sponsoring" company is useful to prove high skill. At

I think H1Bs should not even be required to hold a job at all. The offer they initially receive from the "sponsoring" company is useful to prove high skill. At that point, they get a fixed amount of time in the US and if companies (whether original or other US companies) want them to work, they have to convince them to work with pay, benefits, working conditions, etc. This would put H1Bs on a closer to level playing field with US talent - there would no longer be a bargaining power advantage to hiring from India over Missouri.