That's an easy one: through checked bags on separate itineraries have a greatly increased propensity to go astray, and the agreements between airlines make it clear who handles the complaint (the airline responsible for final delivery) but also who is responsible (in many cases, the airline which failed to deliver the bag to the next carrier). So much of why BA did it (I'd guess 90%) is because they wanted to limit their liability by ending situations which accounted for much of the lost/misplaced bags and was not compulsory for them to provide.

I guess the other 10% is discouraging people from creatively lowering their fares and increasing their options in markets where BA expects (and was historicaly used to) a dominant position but I personally think that even 10% might be a bit of a generous estimate.