They can't anymore in the EU. It's capped to exactly the 0.2% you mention for debit and 0.3% for credit cards.
This is also the reason why you don't see rewards on consumer cards anymore around here.
NAL. It is somewhat complex and involved Amex exploiting a 'loophole' in the EU law, which capped the fees. It revolves around how three party and four party arrangements were structured and implemented. Nonetheless, it was challenged and Amex lost it's appeal and currently open for interpretation, notwithstanding the fees that it has to continue swallowing as a result.
Excerpt: What is more complex is that American Express doesn’t even charge interchange fees because there is no intermediary. There are no interchange fees to cap. Instead, it has to cap its general fee charged to retailers. This will presumably need to be set at a level similar to the total fees now charged to retailers for accepting Visa or Mastercard.
https://www.headforpoints.com/2018/02/08/american-express-eu...
Scheme fees are still unregulated, though, and I assume that these will be the next focus area of the EU regulator(s).