The problem isn't the short-term flow of money, as it has been said previously, the lack of interest from sponsors will be offset somewhat by the increased TV revenue.
The problem is where is F1 getting their new fans from - I suspect F1 is losing a lot more viewers than gaining over the last few years. This isn't because of the rules or even because of Vettel, it's because the older generations which are already hooked on the sport, either stop getting access to the sport, progressively lose interest, or... as the years go by, they pass away (to be extremely blunt); whereas the new generations don't have F1 easily available to them in a world where there's a billion different distractions they can get entertained with.
In a way I kinda understand why they'd move away from free-to-air TV, we're not living in the 1980s where you reach out to everyone that way. I suspect a lot less people are glued to the telly these days. No they need to prepare for the future, which is to kinda do the opposite of what they're doing right now - go for the internet, yes. It needs to be very well analysed as it wouldn't be profittable for F1 to stream the races online for free, and going behind an online paywall may reach less people than a TV paywall for the time being. But the future is there. They need to start doing baby steps in that direction. Put those 2 minute highlight montages on Youtube not F1.com, strike a partnership with them. Put up official 10/15 minute highlights with commentary the day after the race on Netflix, and start trying to get a deal with them for premium live streams. Things like that. Go after where the young people are and start hooking them with little sweets for them to get a little taste of F1, before you have to chase them in a couple years time.
At the moment it's still not a pressing concern as the immediate dollar bills of pay TV with exclusivity clauses (preventing online deals) speak higher. But as sponsorship gets less and less interested, and the number of fans/viewer diminish year after year in the coming seasons, this problem will become obvious. I hope it won't be too late by then.
If that media guy does buy F1 shares and takes a control stake, it might well be that we get a shift in strategy soon. He'll use it to boost his own media channels, not necessarily the ideal media channels for getting fans, but things might improve. Let's wait and see. I don't think the shift to a premium TV paywall is permanent and will last forever, F1 isn't football, it isn't rooted enough culturally as a must-watch-sport-no-matter-the-cost, to survive that way. The core base of F1 devotees (we) who will complain and complain but pay the bill nevertheless as the dedication to the sport is too big, isn't large enough.