But how long are those visas good for? If it's multiple years, then we really need to count how many active H1Bs there are, not the number issued yearly.
... which indicates that about 500,000 H1B visas are currently valid. If those were to all go to tech workers, that would be about 1/7 of all software developers, which is definitely enough to move the needle on compensation, access to entry level jobs, and so on.
There are a lot more technical jobs that require a degree than 3m software developers. There are dozens of different types of engineering and scientific domains apart from software development.
Even if we assume only half of H1Bs are in software developer roles, 1/14 of all software developers is still enough by my estimation to move the needle. Especially because, even just by random chance, there are likely to be concentrations of H1B visa holders in certain geographic areas.
Honestly I think even the quoted 85,000 number would be enough to move the needle, but 250,000 certainly would be.
Just a couple of "thought experiments"... if there are 3M software developers with on average a 20 year career, about 150,000 would be entering the workforce at any given time. If it's true that H1Bs compete with entry level workers for jobs, 85,000 visas would certainly have a felt impact.
Also, about why I think even 85,000 would affect the entire market... even a relatively small amount of additional workforce can shift the balance of market forces significantly. Again, as a thought experiment, let's say there are 100,000 jobs for software engineers and those software engineers are worth $200,000 to the companies that employ them. For simplicity, let's say additional software engineers beyond 100,000 are absolutely worthless to the company. Assuming we have 95,000 software engineers looking for jobs, they find themselves highly in demand and able to negotiate from a strong position for high salary, benefits, and so on. If we add another 10,000 engineers somehow, from any source (including increases in the local training of engineers), suddenly there are more engineers than the market demands, and a race to the bottom could begin (assuming all engineers were equal). Obviously there is also a skill distribution so the most highly skilled engineers would be less affected than those less skilled, but as you get closer to the bottom of the distribution, you'd be more affected by the changes to negotiating power even if you're more skilled than some of the new entrants.
Obviously the above is not a rigorous analysis, which could and should be done, but is just a thought experiment to show that it's POSSIBLE that a small number of new entrants could affect the market.
I just Googled and found this article: https://qz.com/949589/the-h-1b-visa-cap-tells-you-very-littl...
... which indicates that about 500,000 H1B visas are currently valid. If those were to all go to tech workers, that would be about 1/7 of all software developers, which is definitely enough to move the needle on compensation, access to entry level jobs, and so on.