The study that supports the claim that the H-1B program suppresses US tech wages is about 20 years old, and no longer reflects the current reality.
In fact, a 2017 Glassdoor study found that the wages of H-1B workers were 2.8% higher than their American counterparts: https://www.glassdoor.com/research/h1b-workers/
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.