I think that would be the wrong direction for the United Nations. I think the idea of a world state or world government would vest too much power in the hands of a few individuals.
What I do think is that the United Nations should play a greater role in setting standards for national constitutional government. As part of this standard should be measures to prevent the rise of national dictators by limiting the the term of any national leader to a total maximum of ten years.
https://www.researchgate.net/project/Open-World
They should also play a role in establishing an enhanced global economic system which is aimed at easing deprivation:
An interesting, though completely imagined, picture of how such governance might look is provided in the TV series 'The Expanse'. Excellent (if somewhat silly, and fun) viewing, but thought provoking around how earth (and beyond) governance by the UN might actually function.