The idea of Bitcoin is not really understood by many people up until this point. They just knew that it is either a digital currency or a form of investment so I guess it won't be something to flex towards other people if they won't really know its importance in the first place unlike on physical things such as cars, phones and the likes. Those wherein OP have referred to as 'fake rich' are typically social climbers, to be more appropriate. The fact that single thing you own will not make you to the upper class, doesn't really make any sense.
 I the post-apocalyptic scenario, nothing will matter anymore except from food, and other necessities an individual will need to survive, that's it. Things are applicable not only with Bitcoin but to all currencies, if this scenario will meet the reality. Technologies will be close to being useless except for those which will contribute to one's survival but for sure there will no longer be systems in general, that will be functional because that would be a total chaos which will more likely to happen.