I make and receive SEPA payments almost every day, but of course I don't know everything. I know that there are some national apps for instant transfers in EU, but these only work between people who have accounts in that country. And then there are some more modern systems for transferring money within the apps of the banks if both sender and receiver are account holders in that bank.
As for normal SEPA payments, they can be instant, but far from every bank is onboard. I notice this with my customers who pay SEPA invoices. Sometimes the payment is instant, sometimes it takes a couple of days after they've said they've paid it. Except for with Stripe, I've never seen an automated SEPA payment system for EUR purchases, but I'd like to see examples if you have. What I've seen is invoices with a generated reference number that is checked against for payment. This works well for purchases that are to be delivered, but it doesn't work for a service that you want to use instantly, such as Kagi. Imagine the rage of a customer if they have to wait for several days while their bank is slow with the payment.
From the perspective of Kagi I think SEPA direct debits are too much trouble for very little benefit. If they don't use Stripe, they'll have to find another system or waste their time programming it. Also these automatic debits can be disputed by customers without having to give a reason for 8 weeks after the charge. Thrifty Europeans could soon discover how to get a few months of Kagi for free. An automated direct debit is fine for rent or your utility bills, because if the customer makes a chargeback, then the landlord or utility company can easily take them to court. But for international purchases there is no chance for the seller.
However: Rules are completely different for SEPA direct debits between businesses, and the buyer does not have such a right to dispute a debit long after it happened, so I can see this as a good option for Kagi selling to businesses. Where the amounts also are higher and card fees start to hurt.
https://www.europeanpaymentscouncil.eu/what-we-do/sepa-direct-debit
For a horror example: https://redlib.kylrth.com/r/stripe/comments/12o0o1n/sepa_refund_scam_5_x_999900/
All in all I think Kagi has enough payment options for now and somebody who really wants to buy their service can find out a way to do it. I also still suspect that the main problem is with your bank. I have a few European debit cards and they work in any and all circumstances, no matter if it's in brick and mortar retail or any online shop, anywhere in the world. But I've also had European cards that in some circumstances would not work internationally or online, because the bank was a crap bank. Since you're in the Euro zone you can pick and choose from any bank and card provider you want.