You think? For me as a Dutch guy my only though was "literally never".
We have ideal for payments (https://www.ideal.nl/en/payment-service-providers/) and every bank has its mobile app that is integrating via ideal. So all payments on my phone the app just pops up, I do a finger scan and done. All apps are very decent for all normal banking business. I can't think of any use case I would need to trust a third party with my credentials.
Another dutch person here. I can think of plenty of use cases. I'd like to keep track of where my money goes, and have played with programs like GnuCash and Ledger before. The big problem is getting data into them. I have a decent system where I download the CSVs, feed them to a script, and everything gets imported. However this requires me to think about downloading that CSV every month. And my administration lags behind by a month. It's also inconvenient if my system can't automatically identify the receiver, since then I'll have to help it out. Hard to do that when I have to recall where I spent $15 a month ago.
If there was an API I could use to get these details, it would be so much more convenient. Could even build a product around it.
Ehhh, you totally seem to miss the point. It's not about making a single payment, but automating that without any user interaction in between.
Simple example: I want to build a arbitrage trading bot that can automatically request my bank to wire money to some address so I can have my funds on an exchange topped up. That's not gonna be possible without an API.
For me, an American guy, my thought was the same. Normal people don't think about APIs. I gather the target audience here is service providers, but the copy is confusing because it seems to be speaking directly to consumers?
I've got a yearly angry tweet that it's totally ridiculous that in $YEAR we do not have an easy, maybe just read-only, way to access our transaction data from banks. (This is for the Netherlands.)
At this point I'd take the enterprisey German API over nothing.
Now that's an intro!