The issue there is, well..

The game doesn't register you as account-based. It registers you as character-based. It's why you don't share gil or mounts or progression in any capacity. To make personal housing shared with alternate characters -on- the same account, then two things would need to occur.

1) A complete rework on how the game reads and manages data, implementing a new "Account ID" reader to verify what you should have / can do.
2) A complete rework of the Tenant system, allowing your alts to be deemed as 'owners' without breaking the system, as it can only hold a maximum of 3 unique Character IDs at present.

All in all, it sounds rather simple, but I have no clue what computer code XIV uses, let alone the algorithms and ciphers they have in place to encrypt data-packets across servers. It COULD be done, but it could also be too much hassle to put resources in to.