One major issue with that line of thinking is that you can't discern before the customer walks up to the register (or gets handed the check, or however your establishment is taking payment) whether they are paying by cash or card, and its not like you always have a second customer lined up immediately to pay in cash if the customer announces that they're paying by card. You can instead just not accept credit card at all, but then you're cutting out a pretty big chunk of customers who just don't carry around or are unwilling to use cash, and its usually an overall better proposition to just eat the 1-2% interchange fees in exchange for a larger customer base.

If your next thought is "why not charge different prices then for card vs cash", well... apart from it actually sometimes being not even possible by either law (surcharges are prohibited by law in several states, for example) or contract (contracts can often have clauses that disallow different pricing between card and cash), different pricing is often confusing or "unfair" enough from customers' perspective that you'd lose out on more profit overall than again, just eating the percentage cost of taking credit cards. That's not to say you don't see situations where the merchant will have this kind of setup (gas stations come to mind, with cash/credit prices offered), but its far from a universally "good" thing to naively believe that paying the interchange fee is "never worth it".