We have the badge system that encourage users use more features on the site. Does that make sense to give user more reputations after achieving badges like nice questions or nice answers?
Reputation and badges are not simply rewards (and indeed, as rewards they're fairly flimsy when one can earn very real rewards putting the same effort into other activities).
Instead, reputation and badges also (and perhaps more usefully) serve as signals to others, but they signal different things.
At the present time I have a similar reputation to whuber (and I hope he will excuse me mentioning him in my answer), but he has a substantially higher number of "Good Answer" badges than I do (about 5 for every 3 I have, even though I have answered more questions). Good Answer badges are quite rare, so someone holding a lot of them tells you something important about the standard of their answers.
More of the story comes when you look at the tag badges, for example, whuber has a
spatial tag badge, spatial statistics being a topic on which he has vastly more knowledge than me. Knowing that he has that tag badge and I don't might help to indicate his relative expertise on the topic.
There are some users on site that have a large amount of reputation that has been mainly gained from asking good questions. That certainly indicates important contributions to the site, but might give you a different view of their answer to some question when compared to a user of similar reputation which has been almost entirely earned on good answers.
Reputation tells our readers only part of the story. Badges tell another part. Both can be useful in giving users a picture of the likely value of what is being said (if it's not otherwise clear). It's no guarantee of course -- anybody might have an off day and give an answer below their usual standard, for example, and ultimately an answer must stand on its own merits -- but such indications can sometimes be useful.