The housing system in this game was designed to be a status symbol; the lack of sufficient housing is not a mistake, it is intentional.

The goal was always for people to have something to say "I got this thing, look at me, I'm cool". That's why Relocation exists, so people who already have status as a member of the landed gentry are able to upgrade at will, ignoring the restrictions us serfs and peons must contend with.

Free Company housing contributes to this in a really pernicious way, creating a massive source of extra demand, while there are no plans to increase supply, thus making the status symbol even more sought after.