The problem is H1B employees cannot switch jobs easily, and so have greater trouble negotiating raises or seeking other opportunities that are a better fit for

The problem is H1B employees cannot switch jobs easily, and so have greater trouble negotiating raises or seeking other opportunities that are a better fit for them. Employers take advantage of this and offer lower salaries. It's this property of the H1B program that results to decreases salaries among holders, which in turn results in lower salaries across the industry (since a citizen or permanent resident has to consider market rate). If anything, citizens should support increased mobility among H1B holders, since this would eliminate the "dual salary" bases between the two groups.