I worked on Square's payment systems and I agree. Most credit card payments at least go through a merchant acquirer, one or two card networks (they can proxy to one another), and the card issuer. Settlement tends to involve other parties like First Data. Sometimes there are extra middlemen like Braintree.
Settlement is slow mainly because of the ancient technology. Payments are usually settled in batches, which are typically processed once a day, and transferred with some variant of FTP. Since there are a few parties involved, it usually takes a few days for each of their batch settlement jobs to complete. The companies involved tend to be very cautious and slow to change; a lot of them still use COBOL running on IBM mainframes.
> On a blockchain that can happen in as little as 10 minutes
Or a matter of seconds with BFT systems :) I'm working on a BFT system with a goal of subsecond consensus.
But more importantly, blockchain might provide a way to get around the information asymmetry problem that dominates financial value exchange. Blockchain is better in the idea that the entity trying to transact exposes all their cards on the blockchain - if they want to extract value from a transaction it will not simply be because they "know more than you". Power to the people.