Feudalism is a typical result of a society collapse, and these guys are building castles. If you are rich and worried about society collapse, that the most logical thing to do.
More likely a group of people will happily murder them for everything in that bunker. If you want to prep, be a fit male in your 20s or 30s with some military experience, charisma and the willingness to be cruel. Property rights won't exist.
What good is gold when money is worthless? What intrinsic value does gold have in a society that isn’t manufacturing electronics?
It depends on the exact circumstances if crypto, fiat currencies, gold, bullets, or potable water will be the most valuable.
Fiat currency is worthless when the government that backs it fails. Cryptocurrencies are unusable without some global network (i.e. the internet). Potable water and bullets may be super valuable, but they don't make for good currency, and of course, any self respecting bunkers will have a lot of these too.
Many things can be valuable in a post apocalyptic world. But gold is a pretty good candidate. Not only that but it is also a rather good investment now, apocalypse or not.
If the entire society you interact with is concentrated in a luxury bunker, gold is much worse than Monopoly money as a means of exchange.
Not that you would actually need a means of exchange in a society where nothing is being produced, mind you. Rationing would be the key, and rationing is not trade.
Gotta have those in the bunker, strictly for barter. ;)
Ways to make fresh water and food, ways to generate electricity, and as we can all guess, an enormous stockpile of toilet paper.
In the face of true societal collapse, lifetime supply of food is more of a problem than it is a solution.
If I'm too old to defend my food, either all the raiders have starved, or they've started farming.
A nice food forest would probably be the best option. Camouflaged to most laypeople who can't identify plants. Only collectable some parts of the year. Attracts wildlife.
People in large cities have different problem sets than people in remote areas. I don't lock my doors, either. People don't wander by. I'm bordered by bluffs and wilderness.
Food stores can be buried etc. I have buried things on my property in the past for a couple of years, came out unchanged.
Also I just think you haven't thought through many of the problems you presented, most are easily solved.
24h guard? No, I'll make good use of zoneminder, moron detection, loud alarms, and a lot of cameras.
I mean I already have that and I'm not wealthy, for an American.
It's not hard to hide a place underground or in a remote wilderness when you have a lot of money.
Or just somewhere easily defensible, with one path up, that requires heavy equipment to alter.
As a billionaire, I believe I would have built some fortified positions to fire from without much chance of being hit myself.
Also I doubt I'll have any kind of obvious entrance to wherever I am.
Even on my own real-life property (I'm not a billionaire), I'm not just going to be like...in the living room. In an end-of-the-world scenario, I'll be camping discreetly somewhere on my own property, which is mostly a hardwood forest with a pretty dense understory. It wouldn't be any more inviting than hundreds of thousands of similar acres, so security through obscurity is pretty good.
I'll have access to all the tools I need, a house, my own water source. I'm not particularly likely to survive on my own permanently, but I think I've got a shot to wait out a storm for a year or two.
stockpile vodka, coffee and tobacco. problem solved.
Vodka, yes. E0 with fuel stabilizer, also.