[I]ronically, it's not rational to be too rational.This is a position that the Enlightenment tried to do away with, but it's worth noting that even Kant came around to it. While maintaining that ethics was an exercise of practical reason, in the Doctrine of Virtue he ends up describing a number of "moral feelings" that are the ground of caring about doing the right thing at all (Ak. 6:399-403). This was published late in his life, many years after his more famous Groundwork that appears to downplay the role of feelings in morality to an extreme degree.
Imagine that you're thinking of getting married. Would you want a spouse who sticks with you for purely rational reasons, or one who forms an irrational attachment — let's call it "love" — that doesn't depend on rational factors?
Most people would say the latter. A purely rational attachment is nice, but if things change — say, if you become sick, or unattractive, or broke — a rationally attached person might rationally choose to leave. A person who loves you, on the other hand, might stick around anyway, because being parted from you, even if some of your charms have vanished, would cause emotional pain, while helping you feels good.
Likewise, you'd like to hire an honest employee, one who will feel guilty about stealing from you. A rational employee won't steal if there's a danger of being caught, but an honest one won't steal even when he can get away with it, because if he does he will feel guilty, while if he resists temptation he will feel virtuous.
A person who is perfectly rational about costs and benefits, with no irrational constraints like loyalty or honesty (or patriotism), is a person who will lie, cheat and steal whenever he or she can get away with it. A sociopath, basically.
On careful and long consideration, a certain set of feelings are presupposed in caring about doing the right thing. A purely rational being just might not care about going above and beyond the demands of law for the benefit of other people.