Most companies are motivated to return a profit because that's what their shareholders want, and the continued employment of their directors depends on keeping the shareholders happy. The BBC doesn't have shareholders, it has a government oversight committee. The continued employment of their directors depends on keeping that committee happy, which a move like you propose would certainly not achieve.

They have an ordained purpose of providing quality content to UK citizens. Selling content internationally is only done insofar as it furthers this purpose (by generating extra funding for it). Their performance is measured based on how well they satisfy the UK market.

The TV shows have never been any worse than private competition, especially considering the 'original 5'. In my opinion, BBC shows tend to be better overall (except Eastenders vs Coronation St).

That plus no adverts every 15 mins makes for a good experience.

Wrt to news, I read BBC News quite a lot. Again, no adverts to slow scrolling down and reporting that, although may face vehement accusations of bias, isn't all that biased.

I would prefer to keep the BBC too.