Because of the stickiness of prices, passing through of cost savings usually manifest as slower inflation. Costco is rumored to have negotiated 0.3% from Visa in exchange for exclusivity. This is part of how they are able to sell goods at thin markups. Aldi USA used to only take debit cards. They caved and now take credit cards. Travelers Insurance offers two prices on every quote: by bank account or a higher one by credit card.

http://www.bloomberg.com/features/2015-how-amex-lost-costco/

Most insurances do charge lower fees for direct deposit - Allstate does it at well.

Comcast too. I get five dollars off per month for direct deposit. I believe it’s less about fees but more about avoiding chargebacks.

Or conversely they are doing a stealth price increase and shifting the blame to credit card fees. The end result is they shift the cost of banking onto the customer like how some businesses only take cash and have installed an ATM. Then they expect the customer eat an ATM fee. The business avoids chargebacks but the customer has to bear the burden of potential leakage of ACH digits and company errors in debiting the wrong amount.

Do you think prices would remain the same if interchange fees doubled?

If the company could profitably charge more for their products, they already would be, regardless of what interchange fees (or other costs) were.

Raising costs means they need to charge more somewhere or lower transaction. Unless in monopoly situation, price pressure goes both ways.

If competitors can lower prices, whole market eventually ends up having to do that.

During the current inflation companies have used inflation as excuse to raise their prices way above inflation. It may be the same here. Publicly state that interchange fees are the reason for the increase but raise the price by way more than the increase in fees.