Would a world-wide currency be a good idea?
I agree with the members that have voted to close, but I felt obliged to point out an important confusion in the question. The OP writes


  "A single currency with an enforcing entity controlling entity could use this power to help countries in the desperate need to grow,... By
  retrieving in the form of taxes a percentage of each nation's Gross
  Domestic Product... and then redistributing this to each country, we
  would be in fact spreading resources from wealthy parts of the world
  to the poorest in a fair way."


It appears therefore that the OP focuses on issues of global income/wealth inequality, and he thinks that, under a common currency, redistribution would be easier... 

...The OP fails to see that, in order to have a global currency, it would take a "geopolitical will" from the parties involved, which, if it existed, the contribution of a common currency as a "redistribution facilitator" would be negligible.  

One important reason of why we do not have a global common currency, has to do with the fact that we do not feel that much "connected", truly "parts of a single whole". Hence, wealth redistribution to the extent imagined by the OP is not something universally desired. Because if such a sense of being part of a single whole was the dominant flavor of human existence, the desire to redistribute would flow rather naturally from it, and then it could actually happen whether we had a common currency or not.

Now I am voting to close also.