a) Because they don't have to - it's a small market, with little prospect of boosting CE/CW yields out of LHR

b) Because they have to hand over GBP50 or so to EI for each seat sold on the BFS hop

c) Because BA is happy for you to pay the price ex-LHR and have you make your own arrangements on EI, thus reducing the cost/hassle/risk of selling through tickets, and having to deal with missed connection/lost bags

(Once EI/BE take over all the domestic routes, bringing passengers to LGW/STN from MAN/EDI/GLA/NCL, and having them make their own way to LHR for their onward connections, there will be no R classes from anywhere except LHR of course )