In London they do have the logos like the mockup above - its small. I think people are smart enough to understand its a service provided by a company.
Yes, it is more blatant in London than in Copenhagen. But operator branding is less obvious compared to the 80s/90s when private operators used the full livery. Nowadays, Londoners probably know that their buses are run by private companies on behalf of TfL, but they don't necessarily know which one. They don't need to know. In the event of GM franchising, it would be up to the authority to decide what kind of operator branding is allowed. They could ban logos altogether if they wanted.