How?
Loosening restrictions on sponsorships would invariably result in a net increase in the available labor pool, which would put downward pressure on wages for everyone. This is because the program as-is does not restrict people from changing jobs. It just requires a sponsorship. So, what you are really advocating is that people without jobs can remain in-country "off-visa". This is not the purpose of the H1-B program.
So, if you were to allow this, yet still keep the notion of H1-B sponsorship alive, then there would be the source of the net increase of available workers.
Now, you could make arguments about lowering the expense and friction involved for sponsoring companies, which would then increase the appeal of H1-B visa holders and make finding new sponsors easier. That would probably go further in the direction of increased salaries you mentioned, so long as you kept the visa-holder cap constant. But, of course, part of the reason for this cost/friction is to provide companies with incentives to source labor locally before looking to non-U.S. labor markets.
It's a complex problem with no easy solutions.