Should Latin America, Africa and Asia have there own unions.

Yes
But it would be maybe almost impossible to remove the European and American control and influence on all those areas.

Example The African Union
Just to mention one, many African Nations' militaries depend on countries like The US, or Russia, or China.

And that's just one only in Africa. Now you do the same with Asia and Latin and South America.

I guess it could be done but it wouldnt be a lot of fun.

Good question

Africa is already moving in this direction through African Union and the African Continental Free Trade Area.