By your logic, all the folks that pickup trash in India should be allowed to move to America and work at a cheaper price than Americans. I am guessing you are also not in favor of the idea immigration, preferring instead a world where anyone can go and work anywhere.

  Notably, they should be able to switch 
  employers without being deported

Agree. That would fix a lot of the issues. But good luck trying to get that through the corporate-backed H1B lobby that thrives on the uncompetitive nature of H1B.

  H1Bs are taking jobs away from them, 
  which implies that they are interchangeable cogs

In most cases where I have heard that argument, it is someone arguing that their job can't be outsourced out of America. They seem to be right if you have to bring the H1Bs into America to replace them. If you can replace Tom in Cambridge's job with someone in Delhi, I have no problem with that.

  one of the biggest factors in my career 
  is still that I was born in Cambridge, 
  Massachusetts

The solution to that is not to import someone who is willing to work less expensively into your country to replace you.

And regardless, the idea behind H1B was never to create "fairness" between the haves and the have-nots. The goal of H1B is a selfish one: to help America. If it is not doing that, it's time to reconsider.

If you want an H1B-like visa to address the disparity between the Indian and the American developer, have a debate in Congress and create a new category(some would argue we already have many, ie. the green card lottery).

  The market price is a signal - it tells 
  you whether there is currently more supply 
  for an industry than demand.

Agree, but that assumes the market is open and fair. With H1Bs it is not as you yourself point out in your first point.