This is missing something important, which we can see by considering one of the major problems merchants want to solve right now.
The credit card companies charge them ~3% and then give ~1% back to the customer, implying that there is a ~2% net gain to be had by cutting out the middle man. So why hasn't this happened? Because the alternative with the lower fees is ACH, but customers are less willing to give out their bank account number than their credit card number to a random small business.
This is the easy case for some centralized service to fix it, right? Have some large trustworthy company take the customer's bank account info and transfer the money to the merchant for a very small processing fee. But this is the part where your assumption falls through. Once the merchant has signed up for this, the payment processor is the only one with the customer's payment info. In other words, it's hard to switch, and then the payment processor can charge higher fees (eroding the benefit) and the high switching costs also cause the market to consolidate. And because you're tied to a single payment processor, when their fraud AI has a false positive they can erase your business overnight by locking you out and not answering the phone.
Now suppose you don't have a centralized system. Instead, the customer acquires a store of value (Bitcoin, stablecoin, something else) however they want. Customer A can get it from Coinbase, Customer B can get it from Stripe, Customer C can get it by selling something on eBay and accepting it as payment, and the merchant doesn't have to do business with any of these third parties to accept payments from customers who do, because they all support the same transfer medium.
Now you have a competitive market. Currently a new payment processor has to earn the trust of a large enough percentage of the general public for merchants to be willing to use them; a new exchange would only need the trust of enough people to be doing enough business to cover their costs, a far lower threshold. If a merchant wants to switch payment processors or has a dispute with one of them, their own customers wouldn't have to do anything different because the means customers use to convert dollars to tokens is independent of the means merchants use to convert tokens to dollars.
> Someone has to pay those costs for the N nodes on the blockchain - who will it be?
That's the boring question. The interesting question is, can you have a blockchain with lower fees than payment processors currently have? And the answer appears to be yes, e.g. the transaction fee for Bitcoin Cash is around a penny.