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 the government of 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.
Agree. In addition, one of the purpose of Bitcoin is to have a universal currency. It can be used for any transactions but it will still be the traditional currencies that business would prefer as it is less volatile. Also, as stated above, traditional currencies are being run by the government where in businesses are registered in. No country will prefer to have this as a main form of transactions.
I believe that the Bitcoin is still growing and can really affect the currency market in the future. Many people are still skeptical about it. The more it grows the more people will be more confident about it in the future to use it in different transactions.