This threat has so far been regarding baggage only.
I think a key reason why this policy was enforced were due to rebookings/ compensation. Example:

Seperat tickets AMS LHR and LHR LAX both BA
2 tickets = 2 contracts

If AMS to LHR gets delayed BA is not required to assist with rebooking to LAX as the tickets are seperated. In case the next LAX flight will depart the next day BA saves money for hotel and compensation according to EU 261 as BA is not responsible despite the passenger has/had a ticket on BA out of LHR.

If AMS through checks the passenger all the way the passenger might claim BA for assisting if he/she misconnects in LHR.

I'm sure baggagehandling is the less issue with this policy.