Thank you Taslios for this topic as I was going to share similar observations myself and I can add to what you were saying.
GalCiv3 went long way since the first release. Originally it felt pretty much like a wargame - all you needed to do was: build manufacturing planets, build research planets, build few market planets as needed - research some weaponry - conquer everyone on Godlike. No need for diplomacy or building anything else on the planets, no need for anything else to win the game...
Now, there are new elements in Crusade and Intrigue, which add more variations to the formula above, but the political and economical aspects of the game still can be significantly improved to actually occupy more of the players game time compared to the time spend fighting. Still that balance is to be achieved and there are quite a few changes needed for it to be there.
One is that as you said, the United Nations and generally diplomatic interactions with other races are lacking. Why, because there is no economic need for that interaction. Each race should strive to get control over higher number of resources and wealth, but it should not only be required for say ship building (as in case of resources). I think each empire should have costs to operate - each of the facilities, i.e. ships, buildings, constructions, etc... should require money maintenance cost, but also resources to operate. Good example of how it should be done - Distant Worlds. There the ships require fuel, the armies, factories, research facilities might also need money and resources to operate properly. That and not conquest - should be the focus of diplomacy in the peace times.
I.e. trade routes with the specific trading planets (hubs) should be added in to the game, in the similar way as it works in Europe Universalis, where the particular trading hubs control the trade of the specific resources and distribution of that trade in the region and where the trading currents are directed in which proportion. Then distribution of those trade roots becomes a negotiation agenda for united nations and between empires.
Regarding war as it is done currently - I think fighting on the surface should be changed from immediate one turn fighting to continues fight, which lasts several turns. That adds depth to each fight and overall warfare. As potentially you need also to spend say - ammunition for the legions to continue fighting and then you need to continuously resupply them. Which makes it important to manage logistics routes in each war zone.
In regards to citizens and there overall content - each planet needs to be populated with it's own pre-dominant race. Each race has to have a specific view on political system they like, whether they are malevolent/pragmatic/benevolent, relation to war, taxes, what planetary improvements they like, what luxury resources, etc. That all should contribute to overall mood of the population on that particular planets and define if it's productivity/taxes/likeliness of appraisal.