I think it is interesting to follow each of the possibilities to their extreme position and then see which makes more sense. Usually, if you do that, I find you can get a good handle on where the balance should be.
Possibility 1: Free-to-air imperative. As there is little / no competition from broadcasters, payments from TV companies trend to zero. F1 then makes most of its money from advertisers wanting massive exposure. Included in this are car companies and nation states (wanting exposure by subsidising races, so track fees are also high).
Teams get lower % of their revenues from FOM and make the rest themselves. Bigger gap between rich and poor.
ie. the current model with BBC (or heaven forbid ITV)
Possibility 2: Pay per view / subscription channel TV. Greatly increased revenues from television, even though audiences are a fraction of what they would be with free-to-air. Sponsorship dries up into small niches (technology partners), so teams are almost wholly reliant on much larger FOM payments. Smaller gap between rich and poor, centrally managed, franchises essentially.
eg. NFL
Looking at it this way, I think the independence of the teams and their identity is the reason F1 is what it is. For me, the PPV view option kills this by making the teams much more dependent on FOM, until eventually it is more like the WWF than F1.
Obviously, the problem exists because the BBC is what it is, essentially a compulsory subscription channel for anyone in the UK who has a TV set. Anyone who has ever tried to do business with the BBC has eventually come across this problem and they use it brilliantly in their negotiations. "You can't charge us as much as the other guy because we have to spend the license fee wisely."
I would not be at all surprised if in a year's time, the BBC has agreed an extension but at say £15-£20m a year rather than the £40m they pay now. This is in the press because the BBC want it to be, I suspect...