F1 is expensive to broadcast because the fees are so high; Sky get it to pay because there are sufficient viewers willing the pay to watch it, the BBC does not have that luxury. The BBC cannot sell it off to other broadcasters.
Most of the drama shows are sold on to other companies both in the UK and elsewhere, overall these reduce the cost of producing them by quite a good percentage.
News is news, the BBC broadcasts to many other countries, the government seem to find this quite useful especially as it does not cost them anything.
Then there are a large number of programmes which are very cheap to make; just watch on BBC1 any time from 9:15 am until 1 pm and 2 pm to 6 pm. These have quite a large percentage of the off-peak audience; you may sneer at them but then they are not aimed at sports viewers.
Then there are the documentaries, consumer programmes, history programmes, science programmes etc. These are factual, some of them can be sold on, some are not; the one thing that most of them have is the spreading of knowledge in a watchable manner. Some which I have watched this year have been most of the Horizon programmes (what did come before the big bang?), the Plantagenet series, this year's harvest and food production and many more.
Finally we come to the politics programmes such as the Andrew Marr show. This also includes Question Time where politicians and other political commentators answer questions from Joe Public; they are subjected to grilling from the audience which some clearly do not relish, there should be one of these every day of the week, actually meeting members of the public is a politician's worst nightmare.
The BBC also paid for the digitisation of UK broadcasting. This as to free up airwave bandwidths so that the government could sell the various frequencies, bringing them in shedloads of money.
Remember when watching Freeserve that it was the BBC that paid for it for you.