You didn't process my comment fully.
I was referring to the downward pressure on all wages (and U.S. workers in particular), not those of H1-B holders. This (and my entire comment) was a rebuttal of the GP and should be read in that context. Having workers stay in the country without jobs increases labor supply, which means lower wages for U.S. workers, contrary to the GP's counter-intuitive assertion. It's simple supply and demand.
But, in general, what you're describing is not the intent of the H1-B program. The purpose of that program is to allow companies to "import" supplemental labor in certain specialty fields when there is no local talent available.
It is specifically a non-immigrant visa. However, people have subsequently come to view it as an immigration path and, hence the "binding" to a sponsor as unfair. But, if you go back to the original intent, the worker has agreed to enter the country at the pleasure of their sponsor.
Now, if you want to do away with the H1-B concept, allow companies to hire anyone from anywhere, and allow those workers to switch employers at will, then OK. But, you have to call it something else and assess the impact accordingly. That takes us back to increased labor supply and lower wages for all. There are people who don't like that idea.
It's obviously unpopular to say this, but that makes it no less true. And, if you really want to address the abuses or find a more equitable situation for visa holders, then you have to start by acknowledging the current reality.