Given that immigration laws are import quotas, that the free market will fix things is a confused argument. There's no such free market in software engineering labour.
Well, there's freelancing, but that market has serious problems with flows of information. (Which would be worth tons of money, if you could solve them.)
The flow of information between transacting parties is a fairly central problem of economics. It's believed to be why companies exist (since alternatively the logical end point for a perfect free market is a thin gas of individual, rational agents), and it explains the "Market for Lemons".
Solving that problem preoccupies a large part of the economy. And making it worse, another large part. All hail the Red Queen.