It is unstable in that 1) it is a housing option of last resort and 2) no one wants to stay longer than they need to. It is not a place where people "put down their roots," partially by design, partially by circumstances.
In 2015 the average length of stay was 22 years.
In general the idea that folks would wait years on a waitlist with the intent of leaving ASAP doesn’t pass the smell test.
tl;dr: the mean is almost certainly the wrong statistic.
This is one of those things that sounds smart but fails the common sense test.
Perhaps you're right that the gap between median and mean doesn't change the final conclusion. I can't really say at this point.