Those are other, unrelated problems that need to be addressed in their own right, but cannot be used as justification for high pay scale of politicians.
So basically no one expects to make money from their paycheck, but rather go into politics for the fame, connections, and other intangibles.
Position, connections, and influence go a long way before you even commit a crime.
They can trade stock knowing certain laws will be passed or bills introduced that will have an effect.
Look at Harry Reid as an easy example.