The market is segmented between Premium and LCC, that's pretty obvious. If you fly LCC, BA are not particularly good - not as good at BoB, not fantastic prices. So you'll rank them lower. If you're premium you'll have seen a deterioration in service levels over recent years, and you may have flown a better premium product. So you'll rank them lower. In getting themselves caught in no-mans-land between LCC and premium, BA are literally in a no-win position. Not LCC enough, not Premium enough.
Cruz has to decide which model to go for. If he's going LCC, then he has a problem, because it's easier to build an organisation along cost lines (Easyjet, Ryanair, Air Asia) than to change a premium organisation to low cost by cost cutting. Cost cutting inevitably causes ill will amongst employees and customers. I suspect some of the problems with BoB are because staff don't agree with it, and resent the change. If you're low cost, you have to build cost management in at every stage, and you have to prioritise volume over value, Easy enough for a new organisation, impossible when you have trained and selected staff to favour value.
If he goes for premium he also has a problem because the perception now - right or wrong - is that other airlines are better - for example I would prefer Qatar or Emirates over BA long haul given a choice. I'm not that bothered about finessing the price.
Cruz comes from a low cost background, but transforming BA doesn't need that in my opinion, it needs a strategist who is skilled at bringing an organisation with him or her against a clear vision. The muddy vision of two airlines in one plane isn't compelling, it's trying to have his cake and eat it. I have a feeling BA may be notable in coming years as a case study of how to degrade a brand.
"World's favourite airline"? I remember when it was my favourite. I actually got a spring in my step when booked in club, and had high expectations of quality wherever I was seating. Now I fly BA because it tends to go to the destinations I need, and I cling, illogically, to the idea that status means something beneficial. I doubt I'm unique.