I don't think that's necessarily true. The classic example is where car companies create a car together and then put two different badges on it. One is then priced higher than the other based on the brand that's on it, even though they're exactly the same. The idea of brand value is that you can increase your prices purely because of the brand that's on it rather than the cost of making the product going up. You can also have a very valuable brand without being the most profitable organisation in your field. Cambridge University has an incredible powerful brand, but it makes nowhere near the profits of plenty of other educational institutions. But put 'Cambridge' on an exam or a book, and suddenly it's associated with a certain educational standard in a way that a more profitable university might not be.
In terms of football clubs, I guess the strength of the brand would be based on how valuable it is for companies to be associated with City. If they can put 'official sponsor' and a picture of Haaland and De Bruyne in their advertising, how much is that worth, and how much does it compare to other clubs? And that may be based on history and fanbase, but it's primarily based on sporting success, because brands are more interested in associating themselves with current elite sport than formerly elite sport. Otherwise Michael Jordan or Mike Tyson would still be the highest paid sportsman in the world. But that doesn't mean history plays no part. I'm sure Michael Jordan could still command more money than the majority of current NBA players if he was to do an advert. And you see teams like the New York Yankees who have an incredibly strong brand based mainly on historical success, and basically being able to create a fashion brand around their logo. In a sense, a football club's brand is arguably a bit like accreditation. Like how valuable is it to have the Fair Trade brand on your packaging? How valuable is it to have a little City badge on your packaging?
