That's the thing, they're already in the US. They've been here for years if not decades. They just don't have a green card or voting rights. You either also implement a per country cap on H-1B or remove it from green card altogether. This business of having it on the green cards (which gives immigrants their rights and bargaining power) but not on H-1B disproportionately tilts power in favor the companies.

Tech companies get to have their cake and eat it too under the current system. In other words, business as usual...