Re: A false argument
If we do leave (in my view, we should stay), what is to prevent those workers from still working in the UK? Nothing from the EU side of things.
I think you are mistaken. I am allowed in the UK under current rules, but if the rules change and I want to have a guarantee that I can still work here, I will have to apply for British citizenship or work visa, or rely on some other deal in which I have no say (but HM Government will) - all of which will subject to me stricter checks than quick look into my current passport. Currently few EU citizens working in the UK bother with citizenship, since it is not needed for anything. With UK leaving, this will change - and personally I think that's a good thing.