"World currency" may not be the best terminology.

"A monopoly over the entire world's money supply."

"A centralized market of currency, bankers like the Rothschilds have 100% control & ownership over, with no competition."

It may help to know one world currencies and one world governments have a few things in common.

Imagine the entire world is owned and controlled by a single government, which has all of the power. And this single government has full control over the only currency utilized in the entire world. The keyword with this arrangement may be: control. This type of centralization of currency and state makes it easier for a shift towards totalitarian rule. But it could have significant drawbacks in terms of centralized control being a very poor format for producing innovation/progress/etc.

Under a totalitarian rule, these and many other types of free market innovations do not occur: