Homeowners are buying into houses that have inflated market rates because of the surrounding rent controlled units (same segment of the population fighting over inflated homes/apartments). Yes, it's difficult to move if you own a home -- you need to arrange buying and selling and transferring assets and all of that. However, you actually have more freedom to move to an area that does not have rent control (cheaper average home prices, all other factors considered), or move to a similarly priced home in the same general area.

You're trapped for logistical reasons that are surmountable with a little work. You're not trapped in the sense that you absolutely can't afford to move anywhere else in your city, because of overinflated residence costs.