I know all of that. I was one of them. But you got things half-right. If it were easier to companies to sponsor H1B visas, it would also mean that it would be easier for me to switch companies if I wanted.
I got a H1B outside of the quota (education/not for profit). The industry I was working was probably paying 10-15% than I could get if I got a job at a tech company, but not any lower than a startup. Every startup I interviewed was paying the same or more than the job I took. They would gladly pay whatever I asked. The problem was in dealing with the bureaucracy of immigration. Most of the fear of switching jobs would go away if foreigners knew they could be easily hired by small/medium-sized companies and startups.
The most honest and fair thing would be to grant the visa for a time period, and let the visa holder negotiate with companies like any other citizen.
But thats not what this recent 'reform immigration' movement is about. When you get down to it, the tech immigration movement, FWD.US, is basically asking for more H1B visas to be allocated, which will give the biggest companies even more of an advantage against both competing small companies (that don't have a legal team dedicated to immigration) and employees (who can't negotiate against captive labor).
Thats why it's basically composed of huge companies, and you don't see much buy in from smaller ones.
I got a H1B outside of the quota (education/not for profit). The industry I was working was probably paying 10-15% than I could get if I got a job at a tech company, but not any lower than a startup. Every startup I interviewed was paying the same or more than the job I took. They would gladly pay whatever I asked. The problem was in dealing with the bureaucracy of immigration. Most of the fear of switching jobs would go away if foreigners knew they could be easily hired by small/medium-sized companies and startups.