I'm unsure that the population density is a good measure, as it implies that if a country manages to get their population down they lose control once more. I can see it is useful to compare countries, and show some have more room than others in which to place incomers, but that's about it.
Also what is the definition of a quota ? It should describe a limit, but who dictates how that is applied ? Can a nation say they will take no more than 100, and end up after vetting each application allowing only 5 in, since that was not over the limit and so within quota ? Or does the EU demand that since the quota was 100 they will force the nation to take 100 whether the nation likes it or not ? Which, of course, is unacceptable.
I suspect it would be read not as a limit, as it should, but as an obligation. That control of one's own borders would be more or less an illusion for all practical purposes. But anyone who agreed to such a scheme would almost certainly claim to have achieved something, but would only fool themselves, and probably not even themselves.