this is such a great point and I wish it was talked about more in the discussions of these issues. rent control basically traps people in a single apartment for the rest of their lives. it traps their sons and daughters there too (if they elect to "inherit" the apartment, which they frequently do).
this is one of the ways that ghettos come in to existence. the ability to move to somewhere else is really fundamental to preserving a person's freedom and quality of life. rent control takes that away and replaces it with a market dislocation and transfer payment.