I don't think they artificially limit their supply. I'm not a lawyer but I'm pretty sure you need to pass a fairly difficult exam and maybe need some formal schooling?

That's going to cut down on the supply of lawyers.

Programming can also be done remotely. Having someone working in India where the cost of living for them might be 50x less than NYC is going to result in them working for a cheaper price than a programmer in NYC.

You can't really hire a plumber or lawyer from another country and expect them to be able to do their job remotely too.