The problem with the BBC including advertising is that it will compete with ITV, Sky et al. So everyone would share a piece of the advertising pie with knock on effects for all of them. It would be hard to know how David Attenborough's programmes would be financed.
It's not a planned economy, that's not how it works.
I feel like I'm repeating myself (over and over and over again) but life outside of public broadcasting is not just the Real Housewives. Business can and will support risky, high-brow, high-quality, big-budget programming.
If we follow the US model there are many instances there where pressure from advertisers has caused programme cancellations or sackings. Margaret Thatcher had a review of the BBC funding and her free marketeer chosen investigator came to the conclusion it was not the way to go.
I think if anything you'd run afoul of advertisers if you breached the kind of political correctness that no doubt BBC supporters entirely agree with, like questioning global warming, or homophobic or racist content. Do you have an example in mind?