That's a circular argument--there are obviously two ways that the share of revenue from interchange fees could become higher than they are now--increase the interchange fees, or decrease the interest rates, membership fees, and other revenue sources (or both).
Higher interchange fees would necessarily "end up resulting in higher costs for consumers" only if the interest rates didn't also decrease. Are you assuming the credit card company's total revenue is a fixed constant?
Or are you just suggesting that if a very large group of cardholders collectively decided to pay off their credit card balances in full every month so that credit card companies didn't make a cent in interest off them, that credit card companies would simply increase their interchange fees to compensate? Perhaps. But then a lot of merchants would stop accepting credit cards. They could face antitrust litigation again. Perhaps they would just add/increase yearly card membership fees, cut back on rewards, lay off customer service staff, etc. Who knows? They make their money in several different ways, and each of those they are already squeezing as much money as they possibly can out of consumers and merchants.
The way I see it, as a responsible cardholder who pays my bill in full every month, merchants and irresponsible users of credit are just subsidizing my free 30-day loans, cash back rewards, and frequent flyer miles, and I'd prefer that they keep doing so.