We really don't know the reasons for the experiments. It is one of the mysteries of Fallout.
Well I have theories that involve Vault Zero's roll in the whole system. But as to why they went through with the Vault Experiments. I would guess that they didn't actually believe there was going to be a nuclear war or any other doomsday scenario.
The Vaults were built in response to New Plague. Built to actually save lives and preserve America. The project continued when China invaded and nuclear war became a real threat. But over time the idea of nuclear war didn't seem that likely and so they found another use for the Vaults.
I also like to think the whole system wasn't in place when the Great War happened and therefore it fell apart and or the damage done was alot greater then predicted and still resulted in failure of Vault communications.
It is possible that there was a plan for rebuilding, but it got all fubar and never happened.