It depends how you understand "trading". If your mean only investing on some exchanges and treat crypto only as way of making money, then yes, cryptocurrencies can exist. We should remember that main goal of crypto is global adoption. If we will lead to the situation when coins will be in widespread use (and this is slowly beginning to happen, mostly in case of Bitcoin, but other coins don't stay behind - for example Dash and FuturoCoin are aiming for this, FTO even has its designated chain of restaurants: https://newsroom.futurocoin.com/next-futurenet-restaurant-is-already-open/) then trading won't be necessary anymore