There will still be immigrants without H1b - but H1b specifically targets tech employees with the fallacy that there are not enough tech workers
saving money on their education cost and getting taxes paid is fine, sure. in the same time you have a local citizen who is out of job. how much money will be spent on him/her (in)directly? from unemployment benefits at first to potential disability eventually, to cover expenses with healthcare or any other payments that would be defaulted.
If anything, these people are coming, paying high taxes whilst receiving only a tiny fraction of the benefits (no medicare, no unemployment, no education cost) etc. They may or may not be driving salaries down (pretty sure if the law was enforced it wouldn't be the case), but you can't ignore the rest.
There's also a lot of statistics on immigrants and children of immigrants founding a disproportionate amount of companies compared to US natives.