Yes and no. The ultimate goal for many H1Bs is the green card - and after your application is in your mobility is severely restricted.

The nature of the country-based priority dates means that Chinese and Indian nationals wait years for the green card application is approved, during which time they (mostly) cannot move.

So if you're strictly on a H1B, yes, it's trivial to switch jobs. If you have a green card application in-process and aren't from China, India, or the Philippines, it's also pretty easy to move (you might have to wait a few months for the right moment). For people from the above three countries it's just pain and misery.

At Hired, we found that candidates who are on H1B visas get 1/3rd fewer job offers. So yes, technically transfers are easy, but you definitely reduce the number of potential employers.

Body shops typically lock employees into restrictive contracts where punitive relocation "costs" are levied if the employee leaves before the contract is up.