Wouldn't this create the obvious problem of companies artificially increasing comp.? How do you judge that? Seems like its asking for trouble. They already do this a little bit with advanced degrees.
Why is that a problem? They wouldn't bring in H1Bs unless there was an obvious benefit. Your "problem" just reduces the gap between value produced and compensation.
Yes, they would increase the compensation until they were paying the same rate they would need to to hire a citizen (which should already be the case, in theory).
I'm saying the company would try to "artificially" increase the value of compensation without adding anything that really is valued at the price they say it is. Think extra benefits, not increased salary.