"You can only stay in the country if you're sponsored by an employer" creates an environment where workers have low bargaining power, decreasing the pressure for good working conditions (e.g. high pay), which – among other things – has impacts on the working conditions for locals. One might say it "affects what the market will sustain" (personally, I don't think calling everything a "market" is insightful).

From a purely economic perspective, the ideal is no borders, and total freedom of movement – but, of course, there are reasons that people don't want that: the real world doesn't run on economics. Pretty much all of these measures are compromises of some description, with non-obvious (and sometimes delayed) consequences if you start messing about with them. Most arguments involving "$CountryName jobs for $Demonym!" ignore all that, and if that leads to policy decisions, bad things happen. (That's not to say there's no way to enact protectionist employment policies, but you'd need to tweak more than just the one dial if you wanted that to work.)