As others have said, having the whole vault be accessible would be a nightmare, not least because in FOS you can quickly build a Vault that's larger in area than any in a Fallout game to date - hell, mine was bigger than any structure in a Fallout game, period. Even if it was nothing but empty rooms to run through, it'd be a major strain on system resources.

At most, what might be cool is if you find an unmarked Vault door, and upon investigating, someone from inside tells you over the intercom that they're at capacity, and they can't take on any more Dwellers, but would you like to buy some Nuka-Cola? (This option would appear if your FOS Vault has built a Bottler.)

They'd still have to solve the problem of communicating with the app, but it'd be much simpler to implement (as there's no enterable rooms) while still creating a minor incentive for sticking with Shelter at least until the endgame...