The method you state for funding CC rewards is certainly one of those that happen. However, it's not the only way.

Merchants will often absorb the cost of CC transactions as these are guaranteed payments, whereas checks sometimes bounce, leading to wasted time and effort, as well as fees charged by their banks. Thus, spending ~2% to finance CC rewards isn't all lost profit.

Another source is issuers' marketing budgets. Issuers want to gain users (i.e., people who carry and use their cards), so they provide rewards, sometimes far in excess of what the interchange fees cover.

For example, my Shop Your Way Mastercard offers up to 10% cash back reward on gas, groceries, and restaurants for monthly spend levels between $1200 and $1800. There's no way they can cover that through a 4% interchange fee.