My server had no houses available. My FC and I were able to save for one and buy a small one before they added new wards.
We now moved to a bigger one. Same thing, no houses. We just patiently saved money and grabbed one when the opportunity arised.
Now my FC wants to move to Shirogane, and when I raised the cost of moving they all offered they gil. Makes me proud of having such people around :>

Honestly, if you haven't been able to save for a house in a year you weren't even trying.