Not a billionaire but would love to start digging my own tunnels. [1] As for the billionaires, all the bunker's I've seen them build can barely just be called a bunker. Most are mansions and some of them are even carbon neutral.
A bunker won't help if the citizens decide to weld the doors shut from the outside.
If you're a billionaire, no need to be nervous to get a bunker. Spending an immaterial amount of money to stave off rare risk only makes sense. Having billions of dollars is useless if you're stuck in a war of whatever.
Personally I think a bunker is probably a naive solution, but doing something is not a bad move if you have the money