There is another very important reason for this, in my opinion. While the Supreme Court has held that, for the first appeal only after a criminal is convicted, they have the right to counsel, even if they cannot afford one. In short, the government will provide them with a public defender free of charge for the first appeal only. In legal terms, this is known as a Right to First Appeal.
After that, the convicted are on the hook, financially, for their subsequent appeals. An average appeal can run in the tens of thousands of dollars depending on the case, and many do not pursue appeals that might even have legal grounds for the simple reason that they or their families cannot afford it.
There are a number of reasons for this. Here are the two that are most important:
First, most people who are found guilty actually are guilty. If a person is factually guilty, he is going to be less likely to try to appeal his conviction.
Second, appeals are only possible on legal grounds, not on factual grounds. A person who feels that the court simply made the wrong decision has no grounds for appeal. The appeal is only possible if the judge has made some error in applying the law. This takes away an avenue of appeal that many would like to take -- the one where they just argue that the jury was wrong.