Think about it; the government is gone, there’s no gasoline or power of any kind, no way to get food.

That kind of complete collapse, world-wide is unlikely. Gold could be useful if a country’s currency collapses, which does happen sometimes. Gold dealers will still exist and they can sell it to other countries if they have to. Central banks do buy gold for various reasons. Though, gold is super volatile and highly speculative compared to central-bank currencies (usually), so I don’t really trust it as a “store of value” or currency. Gold has the reputation it does mostly for traditional reasons. Theoretically, any rare, expensive to mine/acquire resource could take its place if enough people/institutions agreed on it.