Short of an ASB, I doubt you'd be able to get the great powers to hand the United Nations actual teeth to enforce anything with. I'm fairly sure the only reason it worked in Command and Conquer was because, following from Red Alert, there were no Great Powers in opposition to each other left - the Soviet Union had been defeated (or, going by some in-game cinematics' background chatter, the founding blocks were laid during the war and the Soviets were basically a rogue state anyway). But even that's a bit of a simplistic approach Command and Conquer took; I don't see anything like the Global Defense Initiative arising, especially not today.
Further, I doubt the existence of such an organization would really prevent the Rwandan genocide, terror attacks or Daesh. It wasn't until the Second Tiberium War that GDI really became more than just a reactive force, and that was largely due to an ongoing civilizational breakdown as a direct result of ecological disaster caused by tiberium. At best they'd be deployed after any such group causes big enough of a stir to attract the attention of the United Nations (and boy, is the UN blind sometimes).
Perversely enough, if you do want to prevent many of the aforementioned events, you'd probably want something akin to the Brotherhood of Nod instead. I've always felt the games implied that the Brotherhood often subsumed terrorist groups or insurgencies, and appears to have had something of a talent for making much of the developing world (and all losers of the current global order in general) fall in line, despite previous ethnic, religious or cultural tensions.
Prior to the tiberium wars, it seems like Nod ran itself like a somewhat shady, but rather powerful and influential philantropist organization, providing security and humanitarian aid in third world countries in exchange for access to any tiberium in their territory. Which really wasn't a big problem - dealing with spreading tiberium in itself was a humanitarian effort, and likely one most African countries couldn't have hoped to do themselves due to the cost of specialized equipment.
I don't think the games ever really clear up just how much of the Tiberium Wars really were Kane's plan from the start - the first war did start after a four-week bombing spree all over the developed world by Nod-affiliated militants; which could have happened on Kane's orders, but could just as well be blamed on rogue elements within the organization, given how vast it was.
The Brotherhood did have a problem with rogue elements over its entire history, but normally seemed well capable of keeping a lid on violent civil conflict spiraling out of control - generally by making a rather brutal example of those who did stir up trouble, as two concurrent missions in the Nod campaign of Tiberium Dawn prove. They were generally much less inhibited when it came down to things like civilian casualties, false flag operations or rather barbaric weapons, really.
But, well. Yeah. GDI wouldn't be much help in its early form, and Nod would reduce the amount of terrorism, but instead give you heightened risk of global war by virtue of Nod basically being a non-government superpower. Pick your poison.
I'm not sure if this really belongs in this subforum though. Where to put it instead, I couldn't tell you, but it doesn't feel quite right anywhere.