An alternative approach...
Turn the BBC into a non-profit. It would therefore be freed of the requirement to bow to the Establishment (i.e. whichever party is in power at the time) for fear of being dealt a rough hand in the next Charter Renewal (so for example on the news front could move towards more balance with an aim of impartiality); while it would also be freed from the commercial pressure to produce "safe" programming that would attract oodles of people to watch adverts. By being non-profit, it would be responsible only to its viewers, and if the revenue department was a completely separate division from the programming department with minimal links between the two, it could produce programming for everyone, rather than the top donors. Alongside the change, severely cut back on management roles and replace the crust with fresh meat.
I think part of the problem with the current output of the BBC is that it tries to be everything to everyone, so understandably fails because different demographics have different preferences. Having said that, perhaps they could donate the formats for many BBC3 shows to Channel 4 and Channel 5, and have quality programming aimed at teenagers / young adults instead.
Heck, quality programming and high viewings aren't necessarily mutually exclusive, and needn't be lavish dramas that soak up bucketloads of cash. Even with game and quiz shows, there must be a middle ground between the mindless tat seen across many channels (including the BBC) and those perceived as 'highbrow' e.g. University Challenge, Mastermind. Perhaps take a leaf out of the concepts of Countdown and Millionaire - a challenge that sounds simple, but is deceptively complex. The more highbrow shows also don't need large pots of prize money to motivate the contestants - the experience alone, with possibly something relatively low value such as a mug, dictionary or small trophy as the ultimate prize.