Normally, that’s good advice, but the timings to Düsseldorf on BA are still more convenient for me than Eurowings to Cologne, before you consider loyalty aspects or the quality of the Club Europe product. Even if I had done that, BA would have wrongly refused to honour the car hire booking because they said there was no way to split the flight from the car hire. This means that the booking would have automatically cancelled when I either didn’t pay the balance or pay the difference to combine it with a new flight.
(I also successfully claimed via CEDR for self-help when BA wouldn’t reroute during the air traffic failure in August 2023).