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.
We are still in the early age, and I believe adoption is something we will definitely get to see in the long run.
The problem now is that without some good scaling option, merchants coming in to save the day by implementing cryptocurrencies as a means of payment, government regulations being lenient and then bringing a lot of awareness and adoption, we will keep seeing people look at it towards just being an asset, which is why the market is highly speculative at the market. With real life usage, things would change and as we keep seeing it being used as a currency, it would still serve the function of being a store of value.