The thing is can it ever be well balanced?
Yes, I think it can.
As I say, there's nothing mechanically wrong with the diplo interface. When two humans seek to barter together, it does the trick. Diplomacy need to offer that kind of freedom. The problem is an AI one. And I'm not really speaking specifically about GC3 atm; this is true of most 4xes, which have near-universally adopted the two-menu approach simply because it's the best choice mechanically. It's obvious what everything is, you can ask for most things and trade most things, and it allows you to engage in reasonably sophisticated diplomatic behaviour. Mechanically, it's a very sound model; much more so than any of the alternatives. Adopting something less would be a step backwards, retreating from the challenge rather than overcoming it.
The problem is, of course, the AI. I've never been one to favour making the game easier so the AI can play it when you could be making the AI better. I don't want to play a game that's dumbed down to the point bad AI is good at it. I want to play a good game that the AI needs to be written to a high standard for. And, poking around under the hood, we find that GC3's diplo AI genuinely has been, to some extent.
I'm not convinced that the diplo AI is actually entirely functional - several of the diplo value files seem not to do anything, including the one that defines the AI's acceptance limits - and there's plenty of additional modifiers I'd add to it's valuation calcs, but they're actually very good. It takes account of a really wide array of things, though the values it takes for them aren't really balanced properly yet. It has relations memory, 60+ relations modifiers (which have different impacts for different personalities), and takes up about half the AI defs files. It even applies modifiers to it's valuations in some cases (though it could do with many more).
The big change I'd make isn't a re-work of the whole module; diplo isn't really the issue. I'd just add a couple more relations 'types' to make the AI more three dimensional. The real problem is that it doesn't differentiate between liking someone because you're trading with them and liking them because you're scared of them. The AI is easy to manipulate because it doesn't have multiple motives, like players do; it can't be ambiguous. If we had, rather than just 20 possible 'relations' scores, instead had 20 possible 'love/hate' scores, 20 'fear/condescend' scores, and 20 'trust/distrust' scores, all being impacted different amounts by different actions, then the AI could do things for different reasons. And show them to the player.
So, say we take alliances, for example. Presently, the AI will ally with you once you have relations of over X. It doesn't care how you got to those relations. You could have trade treaties. You might have killed pirates near them recently. Maybe you have open borders. Maybe you inverted the military score modifier and it's scared of you. Who cares? It just likes you.
With a multi-dimensional AI approach, you instead can get an alliance if it fears you OR if it likes you. Either scare the crap out of them, or trade with them and play nice. But that's not all. You can make it more likely to break alliances for multiple different reasons, too. If it's only helping you because it fears you, maybe it will break the alliances more easily. If it likes you AND fears you, maybe it'll still refuse the alliance if it feels you're untrustworthy. Maybe it hates you SO MUCH that it won't buddy up, even though it's terrified of you.
This'd give you the kind of unpredictable, human-like AI that Civ 5 attempted to get on the cheap by just not showing you the active relations modifiers. And it'd let you show the player, so he's not mystified as to why the hell Gandhi just nuked Calais when they'd been getting along famously. He can see the AI's motives, but it's hard to predict them without memorizing 20^3 different relations combinations.