The BBC likes to say that all of its shows are funded by the TV license fee, but Doctor Who makes enough money for BBC Worldwide in DVD sales and overseas broadcast rights to cover its own budget and then some.
Even if only 100 people watched the original broadcast, they would still make Doctor Who, as long as the money is still flowing in.
Ah, no. That would be a breach of the BBC Charter.
The BBC is, by Royal Charter, only allowed to make programmes for the domestic (licence fee-paying) audience. If those programmes can then be sold overseas (or to repeat stations, or DVD, but the rule predates any inkling that they might ever exist) and the money spent on making more programmes for the domestic audience, then that's OK and a nice bonus.
But making a programme purely or even primarily to make profits from sales (even if that money is then used to make programmes for the UK audience) is out. Banned. Verboten. Breach of Royal Charter leading to continued operation of the BBC being technically speaking illegal (and as we're talking about a Royal Charter, possibly treason
). That sort of thing.
It might sound mad - it certainly did back in the mid-1980s when the BBC claimed it was postponing season 23 to save money even though, as Douglas Adams pointed out, it earned more from sales than it cost to make - but the point is that the BBC shouldn't consider profits from sales when deciding what to make, only whether this is a programme the licence fee payers deserve to have. Otherwise it might end up like any normal profit-making TV company, making stuff just because it hopes it'll make money.
PS: On Wormhole's point, bear in mind that a 6 million audience in the UK is roughly the same as a 30 million audience in the States, population for population. How many current US series could match that?