Well Faith is kind of the oposite of Reasoning and I can't see it playing any part in Intimidation so I'd go with Charm. People with Faith may not convince you with logic but the pation in their beliefs can have a kind of charm on its own. For example take the famous quote "When you really want something, all the universe conspires in helping you to achieve it." It has no logical basis at all, it relies on faith. Still it is inspiring for a lot of people.
For Greed I would have to go with Reasoning. The reasonable thing for a person to do is to look after his own interests and the interests of the groups that support him. Of course humans are much more than that, there is emotion, people make choices contrary to their own gain because they care or they adhere to a set of arbitrary values that, though arbitrary they may be, make life more meaningful. That's why so many game theory concepts fail when it comes to real people but work in the case of soulless entities like coorporations or computers. So long story short it is reasonable for a person to be greedy, it's just discouraged by society set or largely accepted sets of values and the conflict that greed can ignite in the persons environment. All that said, if there was say a character stat called Pragmatism, I'd have that give more of a bonus to the Reasoning skill than Greed would. (Greed could still be usefull for a potential barter talent for example).
On your other point I agree that this is a possible side effect. However one has to assume that most people will play the game sticking to more or less some core basic priciples for each character. Not because they have to but because they normally do. Even if a player is all over the spectrum with his dialogue choices he wouldn't be doomed. After all, each of the three dialogue skills would be affected by a number of character stats so such a player would have at least a basic grasp of all three skills. Maybe some stats could affect more than one of them. Add to that that context affects the chances of a choice succeeding and it kind of balances out, if you read the situation right and make the easier roll.
In game like NWN it bothered me that I had to spend my points on skills that either help in battle and exploration or just in dialogues, like diplomacy or intimidate. I didn't like that one excluded the other to a degree. However having two separete pools of skillpoints meant that every character could become an expert in at least one form of dialogue skill and that wasn't ideal either. Since I first saw in videos those stat increases after dialogues I hoped that those character personality stats would be really important. As I see it they are a huge oportunity to create a dialogue skill system unlike anything seen in an RPG before.
Imagine this: You play a session of your favorite tabletop RPG and the game master presents you with a menacing and powerful troll blocking your path. Before resulting to combat (that your low level characters would probably not survive) you can have a discussion with the troll and convince it to let you pass. If you try to intimidate it surely the game master would apply a heavy penatly to your roll. If you try to reason with it the roll may be more or less unchanged while charm would get a small bonus. Then you add your dialogue modifiers to your roll. Imagine though that those aren't dependent on your stats or skills but the way you have behaved so far in the campaign. If for example you have a mage that has proven that he is powerful and ruthless he may get enough of a bonus that with a good roll even an intimidate atempt would work. However it would be much easier for your pure cleric who has faith and compassion and believes that every creature has value to succeed on a charm roll, swaying the troll with the power of her personality. Say that the rogue of the team decides to give it a try. He is a pragmatist and knows about greed and could suggest to the troll that if it keeps blocking the pass it is bound to draw the attention of a local lord who would sent a whole company of troups to dispose of it. It would be much more profitable to go build a bridge and collect tolls from anyone passing. Now trolls aren't generally known for their smarts and pragmatism but such a display of logic may succeed with a moderate roll to convince the monster to let them pass. Then as a last example let's take the fighter of the team that has had one too many blows to the head and is very moody, always changing his mind. He wouldn't with any confidence try any of the above but still if he had some semblance of intelligence left he could judge the situation: A huge troll isn't likely to be intimidated by a band of puny adventurers. Also trolls rarely listen to reason. So he decides to charm it. His atempt may be clumsy but with the context bonus he may still succeed in his roll. Now, especially with the multiplayer component, there is a chance to translate such a system to a computer game.
As I said it is just a personal opinion, it's not an issue of right and wrong. Just something that I'd like to see in a game someday, cRPG or tabeltop.
