Sure - if AA shifted their planes away from LHR-DFW and BA filled the gap by pulling out of LHR-DOH, it would appear on the analysis approach used that BA have a new monopoly on Dallas, and don't benefit from serving Doha.
But from BA's perspective, they get the same cash regardless of the operating airline on these routes, so their 'grip' remains the same.

In the same way, AA could start operating some rotations to SJC by reducing frequencies to CLT and RDU, and BA could cut some rotations to SJC and fill in the new gaps to CLT and RDU. It would seem that 3 routes with no competition are now competitive, but BA and AA would still earn the same amounts from each of the routes due to the joint business agreement.

I don't want things to be overcomplicated, but BA does not have a competitor if that airline is in a JBA - so Qatar, American, Finnair, Iberia and Japan Airlines.