The only way to truly solve the issue is to tie the H1B to the person and let them work freely in the US after a short time.
Opening the flood gates might solve the issues of select individuals and some companies, but it doesn't solve wage depression.
The general belief is that H1B workers are underpaid because they have less flexibility in the labor market. While they can move jobs, it's somewhat tedious and requires both companies to work together to make the transition. It's not impossible, but it's certainly not easy.
If there were less friction involved with moving jobs, people on H1B could shop around for a better positions without worrying about their residency should things go wrong.
[1]http://money.cnn.com/2017/02/02/news/india/snapdeal-india-ku...