I am not purporting that the H-1B program has no effect on tech wages, just that it has a negligible effect due to its small cap relative to the number of tech jobs available.
Any increase in labor supply would have some effect on the wage level in an industry.
The US creates several million new jobs each year on average, and the H-1B cap is 85K, which is an order of magnitude less than the number of jobs created per year. In order for the H-1B program to meaningfully impact the US labor market, the H-1B cap needs to be increased significantly.