To address the last point - if your neighbour can't afford to move because the rent is too high elsewhere then under a non-rent controlled system would the landlord not have raised her rent to a point she would be unable to pay it and would thus be forced to move elsewhere?
(I don't know enough to actually have an answer to this.)
1) move away from rising costs, in literally any direction (pick just about any other place in the world), settle into a home you can afford and move again later if you want/need.
2) Live in a rent controlled apartment, become trapped for the rest of your life in a neighborhood where you can no longer afford groceries, healthcare or a haircut because of the rising cost of living.
(I don't know enough to actually have an answer to this.)