Back to the topic in hand: The UHG ought to be competitive. For example, on a cylindrical world map, the Lanun should want to sail around it first because they are masters of the sea, whereas the Austrin want to sail around it first because they are explorers. The Bannor and the Elohim may want to see the elimination of the AV Holy City, the Bannor because it is Junil's will, the Elohim to maintain the purity of Erebus. Likewise the Sheaim and the Elohim may want to hold Bradaline's Well within their borders for X turns, though for diametrically opposed reasons.
Keeping the goals opposed means that you will always be in competition with other nations to complete your UHG, which makes for better gameplay.
You would often loose this competition because of bad luck. You would be suprised if you knew how many player are really upset if the AI beats them to a wonder, there are even the wildest claims of AI cheating somewhere on the forum. And loosing the race to a worldwonder doesn't decide a game. competition is only good if there is no luck involved and you can make a strategy to beat your competition.