Cryptocurrencies can be designed to be suitable stores of value, with superior security, cost, speed, inflation rates, etc., but for them to actually become stores of value they need high enough adoption to stabilize in value.

Gold and any other global monetary systems in the past didn't pop up overnight. They had to be adopted slowly over decades and sometimes centuries. Given the benefits I think it is only a matter of time before public blockchain cryptocurrencies supplants existing currencies.