No vaults means it's not a Fallout game, plain and simple. They have been at the heart of the series since its inception; you can't have Fallout without Vaults.
Fallout 2 only has Vault 8 the other two vaults are Vault 13 and 15, We saw them in Fallout. Tactics only has Vault Zero. It was not till Fallout 3 and New Vegas that Vaults show up over every hill.
What about private industry ones? Not built at request, but built and advertised like Vault Tecs?
It is possible for other Vaults built by Vault Tec to be in places or by other companies. I would like to see some more. We had the LA Vault and Mr.House's Robot one. I want to see more military bunkers and so on.
Still my point is people want to see the crazy Vault experiments and only the ones that have that are the 122 vaults, 105 of them.
I want to see more Vault Cities. There could be 15 out there.