I do not believe a single cryptocurrency will take over. It will be many, all using the blockchain technology for a variety of purposes, but each taking some power from the current banking/fiat system. Currently Bitcoin is like investing in gold and has the most broad-based support and investment. Ethereum is like investing in gasoline, and has the potential to power many future automated technologies, but is not a proven robust network yet. It will have similar growing pains to Bitcoin as more people and developers pile on. DASH is like cash, with its private and instant sending. It has already been around for a few years, with payed development and a governance system to plan its expansion. All the other contenders will be copies of these primary three in my opinion. For example, take the real life hardware being invested in and developed to make it easy to obtain cryptos: https://www.dash.org/forum/threads/get-your-dash-at-9000-kiosks-in-ukraine.15268/
Whats missing, the other 900 cryptocurrencies. Why would they select BTC, ETH and DASH? Because they are different from each other in their own way, and far ahead of all the other alts in potential.