Aren't the real problems the fact that no one has overall responsibility for promoting the sport, and the people who own the commercial rights have never invested any significant amounts of money back into the product they're benefiting from?
Everyone else involved in F1, teams, race promoters, TV companies, all do their bit to cater for their own particular audience (most of them do utilise social and new media), but there doesn't appear to be any strategic overview - and more importantly no significant investment.
How many $ Billion has Bernie/CVC made from the F1 over the years, and how much has been reinvested in promoting and developing the sport?
Apart from F1 in Schools (which doesn't cost Bernie/CVC anything), what else are they doing to engage with kids to get them interested in the technical and sporting side of F1?
Do they do anything to support or promote grassroots involvement in motorsports?
How much support to they give individual race promoters?
Where and how do they advertise/promote F1?
F1 is very much a business, and I can't think of any successful businesses that don't reinvest in their product and don't support the companies/people who sell their product - in F1's case TV companies and circuits/race promoters.
Unfortunately there's no way for Bernie to directly monetise fans, so as far as he's concerned they're about as important to him as Facebook - all he's looking at is how much he can screw from the next would be race promoter or Pay-TV company.