The downside of the cryptocurrency will be its volatility. The World can't have a currency with a value that changes from time to time. It will affect the Economy and that kind of currency will not stay long. I think this is the major downside of the cryptocurrency.
At the moment this is indeed one of the big downsides. This will probably change once crypto is adopted by the general public. Coins like Bitcoin have a big chance not to be adopted massively because a big part of the coins is in the hands of a small group of people. Other coins will come and replace bitcoin with a better scalable product and a better spread of coin holders. This will not mean that Bitcoin will disappear, but it might have to be adapted to satisfy this demand. The lightning network might facilitate this.