If all the problems in the world were solved, it wouldn't be worth living in. Everything would be dull. There would be nothing to do, there wouldn't be world issues to care about. Besides, if there are no problems in the world more problems would evolve. People would never die because no one would get murdered or die of diseases or old age. That would mean that only for a few years everything would be perfect but soon the world would become overpopulated.

 
Overpopulation would lead to starvation , there won't be enough time to populate another planet which would lead to the end of the human race. Anyway, it is not possible to stop people from finding problems with one another.