Rewards give children an incentive to perform better. They may be inspired to turn in their homework on time and do better on their tests. They might study harder and get better grades because of the rewards they are given. This can all lead to a brighter future because their better grades can get them into college. They may even get into a better college than they otherwise would have, making their future job prospects even brighter.
All of the rewards in the world won't get a child through college. In college, there are no immediate rewards other than the satisfaction of earning a good grade. The issue that some teachers, parents and experts have with rewards is that the child may no longer be motivated to do his best once the rewards system is removed. Children need to learn to do their best because they want to be successful, not because there is an immediate reward dangling in front of them.
Natural consequences teach a child that positive things can happen when she does well and negative things can happen when she doesn't do well. If a child continually fails to study for her tests, then she will fail her tests and might fail the class altogether. Then she will have to repeat it the next year, while all of her friends have moved ahead. Natural consequences give children a sense of personal responsibility. They are responsible for making sure that they succeed and if they don't, then they will be the one to suffer the consequences. This can give a child a good work ethic.
Natural consequences don't give children an extra incentive to do better. Children tend to be focused on instant gratification, instead of delayed gratification. If they are offered something immediately after doing well, then they may be more likely to study harder. The promise of college acceptance and a good job in the future might not be enough to motivate a fifth grader to study for his math test today. Although he will eventually suffer a consequence for his actions, those consequences will be in the future, long after he has forgotten about his fifth grade math class. Additionally, the student may suffer irreversible educational consequences, which he will learn to regret after it is too late to change his ways and his future.