In Europe, payment processing interchange fees are regulated. Debit cards are fixed at 0.3% and credit cards at 0.2%. SEPA wire payments have zero interchange.
That's not exactly true. Payments to other countries within the SEPA must not cost more than a domestic payment. That's usually nothing for people, but businesses may pay.
As an example, the Bank of Ireland charges businesses €0.10
https://businessbanking.bankofireland.com/banking/current-ac...
So an upstart bank can claim zero fees, still have access to other banks without them ruining it for them. But in the case of debit/credit cards, you couldn't start a card processor without being subject to fees.
A flat fee doesn't inherently make more sense either, as the marginal cost of processing a transaction is negligible. The costs come from the infrastructure.
There are many ways they could price it, but relating it to transaction size makes a fair amount of sense, since people making larger transactions are demonstrably able to pay more.