So, you have two issues.
One is the illegals, who don’t compete with H1 type jobs, perhaps in the tourist industry on some of the other work visas.
Second, intelligence, if the H1 by itself isn’t at least an indicator of technical skills(your opinion may vary depending upon the particular vagaries of h1 bodyshop salesmanship), then these are pretty much the very people you want.
Check out the makeup of PhD level employment in America, many of them are foreigners who found their skills very lucrative in the USA, they were allowed entry often through an H1.
Not a mindless free immigration type myself, my career got outsourced during the first REPUBLICAN instigated wave of outsourcing when BushOne began the H1 program.
It was all rubberstamping then, I know, because I moved into the bodyshop business from being a mainframe systems techtype.
My point is we don't need the H1b program. It is just a way to undercut the local domestic pool.
I'd want the smart people to come to the U.S. to stay and become Americans.