I can pretty confidently say that all of Visa+Mastercard is way more than a few thousand transactions per second, I'm familiar with several companies that push hundreds of transactions per second through Visa+Mastercard and there's no way they're a significant portion of their business.
Visa says they process "150 million transactions every day in 175 currencies" (see page 3 at https://usa.visa.com/dam/VCOM/download/corporate/media/visan...). That's ~1,800 per second. Mastercard is smaller, so this would be the upper limit for them. Both combined should still fit into "a few thousand transactions per second".
True. The latest financial report from Visa [1] says 164.7B transactions in 2021, or ~5,000 per second. This number is 3x larger! Mastercard is slightly smaller, but comparable at 140B [2].
Imagine we can achieve that throughput with a single server without breaking a sweat![1]. The number of economic transactions all humans engage everyday including cash is perhaps 100x of that: so just in order of 500,000 TPS or less that feels quite small to be honest.
[1] Yes these systems are complex and very distributed and have lot of checks and balances and the actual transactions apps and DBs are running on infra in hundreds or thousands of servers in DCs all around the world.
On the busiest day of the year at peak hour here in the Netherlands the debit card transactions (creditcards are uncommon) reach just over 700/s. [Search for 'pin transacties per seconde' for news items covering this]
Comparing visa and Mastercard transactions with Bitcoin is something that doesn’t make a lot of sense. Do people really think visa settles transactions between two different bank accounts? Those card transactions can take days to settle.
Slow settlement and reversible transactions are a boon for buyers (and for fraudsters abusing chargebacks to get free stuff). For sellers they're a bit of a nightmare since you never know when money you thought you had been payed in good faith might disappear from your accounts with little or no recourse.
Zkrollups on Ethereum can do a couple thousand tx/sec, without security compromises. The plan now is to use the base layer mainly to support rollups, and use data sharding on the base layer to multiply the capacity of rollups. That should get it to about 100,000 tx/sec. That will be a pretty big change, but not as big as what they just did, and they've already got the design mostly worked out.
I doubt that for credit cards. Carrefour or pick your favorite supermarket chain alone probably generate hundreds of transactions per second worldwide during peak periods, and there are tens of major supermarket chains you've never heard of. Add regular grocery stores, cinemas, etc, I'd be really interested in an order of magnitude, but at peak times it has to be in the tens of thousands if not low hundreds of thousands.
For crypto I was trying to be super generous, I know they're incredibly slow.
Edit: Sorry folks, that claim was based on outdated data! The latest figures for both Visa and Mastercard are ~5,000 transactions per second each.