Ok apologies, it looks like the EU has been continuing to chip away at AMEX via its co-brand cards (including the BA cards) and seeking to bring them into the scope of the regulations. From the link AMEX has obviously been involved in a lengthy legal process with the EU and whilst it looks to have lost its case, it’s not 100% clear that this was definitely the end of the road. That said, AMEX has delayed the EU interchange impacts on itself for a few years versus Visa and Mastercard and so the long-term impacts on its products has probably not fully washed through yet. From most of the articles, they seem to suggest that the BA card with a big annual fee may be commercially viable but the free one is less likely to be so. Also bear in mind that the interchange is only 1 element of a card product’s economics - e.g. annual fee, interest bearing balances, credit losses, fraud losses, card usage outside of the EU where the fees (and hence income) is higher etc.. So it is possible that AMEX may still be able to make the product work commercially whereas the ‘AMEX issued via a 3rd party’ cards were pretty quickly pulled back as soon as the EU regulations initially took effect.

Based on how other airline affinity cards work, I assume that AMEX has a contractual agreement to buy Avios at a fixed price per point with BA and AMEX having joint commitments to generate business etc. and some form of a revenue sharing mechanism - so if AMEX is suffering as the card becomes less profitable, I would imagine BA will also be feeling some of the financial pain at some point.