Not to earn income for the city-states but rather to attract adventurers who would then assist with rebuilding efforts and dealing with local issues (like the beast tribes) because they were also now residents.
It would make sense for Ishgard to offer housing for similar reasons now that the Dragonsong War is over. It could even be argued that it would make sense to become available at the end of the 3.0 MSQ even if the Dragonsong War wasn't over at that point. With the start of 3.1, Aymeric takes over as acting head of state and starts slowing working toward changing Ishgard's policies. Adventurers would be useful in helping to repair damaged parts of the city and as supplemental troops until the Dragonsong War was concluded so offering housing to them at that point would make sense.
Personally I find Ala Mhigo and Doma to be better candidates for any new housing district, especially if the next expansion is going to be focused around Garlemald. I'm not sure how many players would enjoy having a house in a snowlocked housing district for the long term. There are already a lot of complaints about how Goblet looks and Ishgard housing would end up even worse if they designed it true to the climate.
I would see Ishgard as a good place to introduce an expansion of the apartment system if SE ever does add size options to apartments. A lot of the noble houses were destroyed during the Dragonsong War and lore-wise it could be their estates reverted to ownership by the state once the last heir died. In one of the quests, I remember it mentioned that each noble house was expected to maintain a residence within The Pillars in addition to any residences they had outside the city, even if the residence was very modest in size. Those now vacant because a noble house died out could then be sold to adventurers, who would probably be slightly more tolerable as neighbors to the surviving noble houses than having the residents of the Brume move in.