Except, of course, they no longer do.

Amex is paying close to 1p per Avios (I have been told this as a fact by people who know). All of the co-brand Amex cards are now impacted by the EU rules on interchange fees which means that retailer fees - excluding terminal costs etc - are 0.3%. You can do the maths.

The annual fee is split with BA, not sure about the %.

I have never got to the bottom of how the 241 is funded, or if BA just covers it directly in return for getting a chunk of the £195.

There is no logic, as far as I can see, for Amex and BA to remain partners. The current Amex contract has already been ripped up, since it covered an Amex for Iberia (which ended up as a Visa/MC) and an Amex for Aer Lingus (same).

There is no economic reason for BA to stick with Amex post interchange fee capping. At the same time, BA suffers because every BA Amex cardholder needs a Visa/MC as well. Virgin Atlantic is making a HUGE push to become that 2nd card in your wallet (30,000 miles bonus on the paid card at present). If BA moves to a Visa/MC it can get a 100% 'share of wallet'.