It sounds odd and totally wrong, but there are downsides to social mobility. Some of the most famous philosophers in history have discussed it: Kant, Benthem, Aristotle. This article from BBC News discusses the downsides they give, such as physical dislocation (moving to where the jobs are), isolation from family and shallow relationships with friends due to short friendships. Also, if riches are based on merit, then you would only have yourself to blame for your own poverty. Another downside is the things that generate money may be terribly soul draining. For example a banker may make a lot of money putting them into the wealthy class, and an artist may end up poor. So assuming upward mobility is desirable, then the incentive is to have more bankers and fewer artists…is this the best possible world?
While I think that social mobility is very important and vital to human existence, it is an interesting and useful thought experiment.