Some part of the fee is used to insure against fraud. That is obviously related to transaction volume.

I think you mean transaction value ($) rather than transaction volume (#). You are correct, and the value is also the right thing to tax if you are funding 30-60 days of interest-free credit.

Thanks, English is not my first language. After looking at the first few Google hits for "transaction volume" it seems to be confusingly used with both meanings but it's best to be unambiguous.

Unfortunately with the way things are set up right now, a percentage fee is actually the only way it makes sense for processors, who are somewhat at the mercy of banks, who charge a percentage-based fee. So if they charge a flat fee, they run the risk of either losing money if the percentage fee is above their cost, or the business will overpay if the flat fee is a lot more than the percentage fee.

(Note, that applies even to flat percentage fee. That's what happens with companies like Square. They lost their shirt in their flat rate deal with Starbucks, because it cost them more to process the transactions than they made via the flat fee.)