I believe this is a danger to the state so therefore the reason it is not allowed.
With the provisos that aliens could not participate in any of the state's health, education or welfare schemes or apply for citizenship, an absolute right for all people to live, work and travel where they choose would bring only the best sort of liberty/opportunity seeking individuals to live among us.
They would have no choice but to create their own voluntary enterprises, dedicated to providing health, education and welfare to their communities, in the form of for profit and non-profit agencies, the cost of which, would, I hope, be 100% tax (not income) deductible. Better yet, they should be exempt from taxes on any programs from which they are excluded.
In time, they would be so much more prosperous than citizens that many would gladly give up their citizenship to join the ranks of aliens that enjoy the benefit of a large degree of voluntary government of their lives.
And so the state would shrink and, I hope, eventually die via privatization, because of the enlightening example of the immigrants' self reliance.