This doesn't work. It artificially inflates the price of labor, and we've seen what happens when local labor is expensive. Never mind that creating a two (three) tiered society of Citizens and (il)legal Immigrants is the Kuwaiti system. You don't get to vote yourself into the aristocracy.
Make it even more expensive to not use in-country labor, including the vigorous prosecution of individuals contracting or employing illegals as well as individual aiding or abetting them.
Besides, you can argue that "stability" is bad for both employer and employee. Without ties to a particular job, it's much easier for an employee to shop his skills around and find a better job
Really? For the greater part of humanity, including those of us in the modern Roman Empire (the United States), stability is a good thing. It allows long-term planning, a chance to gain the skills that impart flexibility in any economy, and otherwise provide for a mutual benefit.
I thought the American way was to reward ambitious self-motivated people and let starve the ones too lazy to care for themselves.
Wrong century. That might have been true for history up to the mid-20th, but it is not true today (despite attempts to return to the darker days).