Why aren't bank deposits considered a form of bank income?
To understand this, think about what income actually is. Income is money that you get that is yours to keep. You do not have to give any part of that income to anyone. It is yours to do with as you like.
When you deposit money in a bank, the bank is not free to do whatever it likes with that money. It owes you that money and must give it to you whenever you ask for it. Therefore, we would not want to call it income. If the bank lends your money and gets interest on it, that is income because the bank gets to keep the money. But the money you deposit is your money and therefore not income for the bank; it is part of a bank's cash deposits.