Earlier quoted context omitted.
Yes, and you can fulfill this growing demand by raising wages, which is essentially the market mechanism to bring in additional supply. Another way to address this is by importing cheaper labor from abroad. For American workers, it is better to let wages rise than to import foreign labor (which would ultimately suppress wage growth). Therefore, importing labor does suppress wages — as you've essentially demonstrated…
Indeed they raised the wages, and yet supply didn't keep up, and that's the reason for H-1B.
Looking at discussions about the current dire state of the white-collar job market — with thousands of applications per job posting and many months of job hunting, even for individuals with over 10 years of experience — it's hard to argue that we're not currently oversupplied.
Perhaps it's time to reconsider the "supply" side of the equation and do something with H1B.