No, we don't. Well, not all of us and not all the time.
For example, I can answer about 70% of javascript questions without any extensive googling or even trying to test something in console before answering.
Javascript is a popular language, and, if I'd choose the way of being JS guru, I will pretty fast become way more close to established user than I currently am.
But the thing is that I find most of these questions boring and, since there are other guys, lot of other guys, who want to be the fastest guns in town, it is OK, nobody cares about me keeping silence :)
On the other hand, to be honest, I'm not that altruistic and the main reason I'm answering the questions is not the will to help. Some answers just help me to find out (or to recall) some interesting information, some answers (mostly "publicistic" ones, on non-technical questions) help me to discipline myself and to upgrade my skills of project manager, which I am in fact.
As for reputation, I very much appreciate this gamification of communications process, and I do like being up-voted, but will do nothing just to be up-voted. Give me my 50-200 rep points at month, and I'm totally OK with it.