As a former H1-B, I might be able to help.
You can change jobs as an H1-B: In fact, I did once, when my first employer was doing constant rounds of layoffs, and I got antsy. It's not easy, as many companies won't sponsor H1-Bs at all, but the real kicker is that most H1-Bs, me included, wanted to stay longer than the 6 year maximum.
We see H1-B as the one way to stay permanently. First you get an H1-B, and maybe in the middle of it, or at the start of the second one, you get your company to sponsor you for a Green Card. If you have real qualifications, it's a very high probability process, but it's very slow. Back when I did it at least, it was VERY, VERY slow. During the process, you can keep renewing your H1-B a third, and even a fourth time, past the 6 year maximum, so barring the company going belly up, or a layoff, you'll eventually be able to stay forever, and get paid real market rates. But during the process, changing jobs is very hard, as changing jobs at the wrong time can make you have to start the process all over again. You might also have had to sign an agreement paying back the costs incurred if you leave before it's all done + 1 year, and that can be 15K, easy, so it's a big deterrent to change jobs.
In my case, I had mild salary increases while I was getting the green card. Now, 3 years later, I make more than double what I made then, in the same town, because now I can actually negotiate without a sword over my head, and change jobs if there is a high enough bidder out there.