Has it happened out of goodwill? Yes. Is it a guaranteed aspect of doing business with BA? Generally not. It may be that the fare difference change is cost-effective, and what does sometimes happen is that if you ask for a free move and the answer is no (which I would expect here unless there was something really unexpected), then the agent may nevertheless be able to find an inexpensive way to do something similar to your request. I think there's always a case for cancelling for a full refund if realistically your trip is too drastically changed, since cold hard cash does the best arguing here. Particularly on a route like Dubai where there are now LCC options.

If it helps, even if you asked at the time of the initial re-routing, it's by no means guaranteed that BA will extend the trip, not least because availability could in the moment be quite tight.