They could theoretically, but it is unlikely due to each transaction costing a few cents and the monthly FedNow fee being $25 (it is a utility run on a cost recovery basis). No banks charge for Zelle payments to my knowledge, for example.
This eventually replaces checks, money orders, Zelle, Venmo, ACH, and probably credit card payment volume over time (as seen with UPI in India and PIX in Brazil). Every deposit account can send to other deposit accounts instantly.