Without being aware of it, gb, you provided an excellent description of how the human theory-of-mind works, and why evolution favored its development.

By choosing to display or not display certain emotional signals, a human manipulates the state of other minds. That's what it's all about. Humans, prehumans, hominids, and primates all live(d) in a social context in which how the other members of the group feel about you and behave toward you is the single most important factor determining whether you thrive or starve...and ultimately, whether your genes are propagated or culled. The more accurate the theory-of-mind, the more often the manipulation succeeds, and the better that individual carrying that mind performs.

Affecting the bystanders is an interesting side-effect. In the context of a social group, disputes are never just between two individuals. Everyone observing the dispute is drawn into it by their innate empathy, to vicariously feel the emotions of the participants, and usually to take sides. Social primates know how to play to the crowd, to try to gain support from the group that will improve their status and ultimately reproductive success.

This is an election season. Watch the debates and you see this phenomenon in action.

As for whether it's intellect or emotion that provides motivation, I think you're confusing a goal with a motive. The intellect can define a goal and the means to its attainment, but that only pushes the question back a level. It doesn't explain why the intellect would want to seek the goal. "Want" is an emotional impetus, distinct from "need".

One of the most dangerous things about elevating logic over emotion is that, taken to its logical endpoint, there's no logical reason to even care whether one lives or dies. Isn't it all futile in the end? Don't we all die eventually? Isn't the human lifespan essentially zero compared to infinite time? Does it therefore really matter whether one dies now, or later?

The intellect says that death is just a thing that inevitably happens. It's the emotions that scream "holy shit I don't wanna die!" and kicks the individual in the ass to run away from the sabretooth tiger and dodge the bullet. Only then does the intellect kick in to decide which way to run or hit the ground. Emotions are the horse, logic is the cart. Get them backward and you can't go anywhere.

It's not about whether logic or emotion is "better", or whether they're in some sense equivalent in importance as your final paragraphs imply. They're completely different, apples and oranges, and the trick isn't to quantitatively balance them or trade them off against each other, so much as it is to have each in its proper place, performing its proper function to your maximum benefit.