I'm not convinced the marginal gains (that was derided endlessly in skeptical cycling fan circles) are really the top shelf issue at United. For sure there's signs the training environment or framing could be improved upon (from the debate around Carrington or the rash of injuries) but I feel the problems are more fundamental (choice of recruits, team building, use of money, etc).
As you note it's a taller order to implement in football. IIRC one of the signs of hyper commitment to elite performances in cycling was having enough laundry machines following the team bus on Tours to efficiently wash jerseys for all (at USPS or Sky, I'm unsure). The price of entry to run a rich cycling operation, including rigorous scientific training, is a lot lower (50-60m a year all included now) than football -the revenue is thinner too, obviously-.
All that said, I was mostly saying that because Brailsford is a cycling man, long a huge figure at Sky/INEOS road cycling and he probably know most of the riders, DS or riders still. So when he's dropping on the Tour de France -as he did this year-. I can certainly imagine that if he offers tactical guidance even outside the scope of his current theorical job, no one is going to shut him out.