I agree with the sentiment, but fairness is still a laudable goal even if it's not perfectly attainable in all facets of life.
The calculated statistics don't guarantee anything, but if you believe in math, your odds are necessarily better over the long term in a point-based system compared to a purely random system. If you wait long enough (and live long enough) in a preference point system, you will get your tag. If your goal is too lofty though, you may die before you get there. But you may also die before you win the lottery in a high demand random draw.
I think some states do cube bonus points. In my model the orange curve is a simple bonus point system (exponent = 1), and the blue curve is bonus points squared (exponent = 2). Increasing the exponent makes the draw odds curve lower and flatter on the front end followed by a steeper climb. As the exponent increases, the bonus point draw odds curve and the ensuing results will more and more closely resemble a preference point system. If you applied a sufficiently large exponent to bonus points, you could replicate exactly the results of a preference point system.