The current law stipulates that no more than 65,000 H1-B visas be issued each fiscal year. As of July 18, only 20,500 of these are filled. Of those, around 12,800 hold a Master's degrees. Are you suggesting that stopping the H1-B program is going to improve employment in US? No. What you'll be doing is reducing the quality of workers in American workplaces.
As regards to removing taxation, I am somewhat ambiguous. One could argue that since H1-B holders are not eligible to receive Social Security benefits, so they should not pay taxes However, a significant number of H1-B holders stay on to obtain a green card, making them eligible for the said benefits. Personally, I have no problem paying the Social Security taxes. The job that I am going to start in a month or so is fairly high-tech, the work is very intellectually stimulating and is simply not done in my home country. I am more than happy to help the currently unemployed Americans by paying my share of taxes. I view this as a price I pay for the better living conditions and greater job satisfaction. Mind you, that does not mean that either of them will be able to do my job. If any American is as skilled as I am, he won't have any problem getting a similar job position as mine.