Many people consider volatility as a drawback to accepting Bitcoin for payments. However, if Bitcoin is widely accepted without any relationship with the fiat, a business or individual would not worry about losing any portion of their payment. There would be no need for anyone to sell Bitcoins, trying to turn them into fiat, in order to use them to pay bills.
Everything would be paid in Bitcoins. No middleman, no high charges, no delayed payments, no chargebacks.