To be honest I don't see much sense in world government creating cryptocurrency that will nearly just like the usual currencies (as TS described it). Cryptocurrency was created exactly for making financial operations without banks or governments interruptions, to bring it out of their control. So why would the world government create it's own cryptocurrency especially it will have no differences from usual fiat currencies?
B/c they would be able to track every transaction and it is a way for more control over people which is essentially what they want. (The way they think is that it will be good for everyone and that is what they will sell to the masses, ease of use just like a visa card) When you travel internationally, you do not need to do an exchange to another currency, you do not need to worry about taxes as they will be automatically deducted from your digital paycheck.
They would be able to detect money laundering, illegal and suspicious transactions, investment gains,etc...