Will bitcoin eventually dominate the world economy and replace traditional currencies?
No, bitcoin can't "replace" traditional fiat currencies, Bitcoin is a form of currency without a third party control, and as you know countries are being run by a government, so it's not possible for a country to function with a currency that they cannot control or print such as Bitcoin, and it's also not possible for there to be no government, so this situation is not possible.
As a result many individuals are beginning to see Bitcoin as a safer investment than its counterparts.
It's true that more individuals and corporations are getting involved and adopting btc for one reason or the other, but mind you that it doesn't still make Bitcoin a 'safe haven investment', nor does it take away it's volatile side, Bitcoin is on a very interesting spike atm, and I hope most of the newcomers to the network wouldn't fright when there's a minor fall in price.