If the wages are rising that means demand is greater than supply. Tech companies are telling the truth when they say there is a shortage of workers.
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 yourself.
Raising wages is probably the last option on the checklist.
Perhaps it's time to reconsider the "supply" side of the equation and do something with H1B.