Let's start with whether non-engineers should subsidize the salaries of engineers through implementing protectionist policies at their own expense in terms of more expensive products? This isn't an obvious answer. Presumably, protecting the salaries of engineers through strict immigration policies also protects the salaries of doctors, factory workers, accountants, taxi drivers, bankers, lawyers, teachers, agricultural field workers. In other words, doesn't it protect the salaries of everyone, across the board?
Does the cost of excluding foreign trained engineers end up being paid back to everyone when their salaries get subsidized as well?
What do people do with their salaries? They buy services and stuff, and the vast majority of the costs can be traced ultimately to expenditures on labor. In fact, it is counter intuitive, but greater capital efficiency in terms of automation and software for example (developed by engineers) makes the non-labor inputs relatively cheaper in comparison to the labor inputs, and explains why real income and measures of quality of life have surged over the past 50 and 100 years.
How do we know that it isn't just an act of faith to believe greater competition for wages doesn't hurt people more in terms of lower salaries than it helps them in terms of decreased costs? That's a comparatively simple answer—people are only hired if the opportunity cost of not hiring them is greater than the cost of their entire compensation package. In other words, if you make $100k in your job, someone who managed not to go out of business is under the impression that not having you would make them lose out on more than $100k of revenue.
Economic growth comes from a greater number of transactions, where the surplus value from what the work is worth is greater than what the effort is worth. Growth does not come from constraints on supply. The immigrant who is paid $80k for work worth $120k takes out $80k, but contributes $120k of work. The original worker, took out $100k, and contributed the same $120k. The aggregate economy is $20k richer, and it is spread out to everyone, because consumption and production balance out.