Ummmm...yes? Is this a trick question?
I see the attraction of extrinsic rewards. HoneyFern took a field trip to the Justin Bieber movie, with the caveat that we would go nowhere until morning work was finished (and it was an extensive list). Work was finished and fantastic, quickly. There was no cajoling, wheedling or "do it or I will say 'do it' again!" It was very clear cut: finish, or we don't go. They finished.
If we continue that path (which we won't; this was an isolated incident), how big would the reward have to be next time?
Daniel T. Willingham addresses the question of learning for its own sake from a cognitive perspective. The article is a bit outdated (2008), but the basic premise is not. He says,
"Rewarding students is, from one perspective, an obvious idea. People do things because they find them rewarding, the reasoning goes, so if students don't find school naturally rewarding (that is, interesting and fun), make it rewarding by offering them something they do like, be it cash or candy.
In this simple sense, rewards usually work."
"If you mistakenly offer a reward that students don't care for, you'll see little result. Or, if you reward the wrong behavior, you'll see a result you don't care for."
Rewards work in the short term, absolutely (see above movie example), but
"It is absolutely the case that trying to control students is destructive to their motivation and their performance. People like autonomy, and using rewards to control people definitely reduces motivation."
"The key factor to keep in mind is that rewards only decrease motivation for tasks that students initially like. If the task is dull, motivation might drop back down to its original level once the rewards stop, but it will not drop below its original level."
The upshot of the article is that extrinsic rewards do not appreciably increase motivation long-term and have potential to be "damaging" in the short-term. If this is the case, why bother? Yes, we may get an easy result, but the result may not be replicated, students may begin to expect rewards and not work in their absence, and teachers may need to come up with increasingly complicated and attractive rewards.
Intrinsic reward, the "reward" of doing one's best because it is what one should do, provide longer-lasting (yet somewhat less glamorous) effects, but this should be the business of education: helping kids become curious, hard-working and persistent in pursuit of knowledge and skills. This obliterates the need for hollow praise and trinkets and instead builds satisfaction and authentic self-esteem, both imperative for teaching confident kids.
But it doesn't preclude the occasional Justin Bieber outing.