I have a feeling I'm about to ramble all over the place, so feel free to tl;dr me.
I think it's always appropriate to reward skillful play, but the reward shouldn't be something that confers (only) advantages in competitive play or something that is unavailable to unskilled players.
In competitive play, this can often fix itself because everybody guns for the player with the advantage. For example, when I played Action Quake 2, getting multiple kills on one life would grant you a score multiplier that doubled every so many kills until you died. In a score based match, this made you the main target. The mechanic made staying alive more desirable, and since there were no health pickups, it made the game more intense. I think this is a good way of rewarding skilled play.
For a different example, consider powerups. If it's possible to grab a damage increasing item or better armor, then it's usually up to the level design to balance things. If it takes skill to reach the powerup, there's typically a risk involved. The powerup may be on a narrow beam across a lava pit that someone could easily knock you into, or you may have to hurt yourself with a rocket jump to reach it, or it's simply out in the open and it'll be open season if you try to go for it. I don't have a problem with this kind of thing. In fact, I enjoy it.
Then there are rewards that try to combine the above two. You get four kills in a row, and you get a free powerup. This is the kind of reward that makes no sense because you get it by demonstrating that you don't need it. A powerup sitting on a pedestal is available to the guy in last place, too, and can even the odds. A score bonus gives the player both a benefit and a detriment, since he's got a bullseye painted on his forehead. Unreal Tournament had the right idea. When you get multiple kills in a row, the announcer proclaims it in a booming voice, and that's more than enough. Playing skillfully is its own reward.
I've given a lot of thought to rubber-banding. I don't mean the way people in the back go faster in Mario Kart, although that's a (poor) case of it. A lot of games suffer from the snowball effect. Something that happens in the first five minutes of a game can determine the outcome, but the game may take another hour to resolve. In an RTS, for example, you might lose a resource gatherer in an early raid, and the amount of resources you're not gathering after that has an impact on everything that happens later. It might take you another few minutes to get to the next tech level, which sets you back even further because you can't expand as early, so all the resources you're not getting from that expansion you haven't built pushes you further behind. Essentially, you lost right after that first raid on your resource line. The game rewarded the player who was able to put together an attack force more quickly, but clearly that player already had an advantage in skill (arguably, depending on the game) and did not need that benefit. There should have been something in the game to give the weaker player an opportunity to recover.
In noncompetitive play, I've repeatedly argued against locking away parts of the game behind challenges many players won't be able to beat. I like the way Blast Corps did it instead. If you got a gold medal on every level, the game challenged you to go for platinum. The only reward for skilled players was another layer of challenge that weaker players wouldn't get anything out of in the first place. There weren't any vehicles that made some of the challenges easier. There weren't game modes that were fun to play around with regardless of skill. There weren't even any new levels. And if you got all the platinum medals, your only reward was the game saying "You can stop now."
In RPGs, which I guess is the real point of the original rant, it's trickier. If there's no reward, some people will still complete the hard side quests because they're there, but most people would feel robbed if they didn't already know there was no reward. I think there should be a reward, but it needs to be something different. A little development of a minor character works well. It could be something like the ability to repaint your airship or redesign your rebel base. There are really quite a few things they could use as quest rewards that would encourage players to complete the quests but wouldn't unbalance the game.
(I'm more opposed to side quests designed to sell the official strategy guide, personally, but that's a different rant entirely.)