The whole BC ethos stems from Lottery funding, which is predicated on winning medals at the Olympics, hence the focus on track cycling. This has its pros and cons - on the one hand, it has hampered the development of the road career of certain riders, but on the other hand, some of those riders might never have got into cycling at all without BC's support.
Don't forget that when the development program was started in the 90s, you could have counted the number of British riders in the Tour de France on the fingers of one hand, and the idea of a Brit winning the Tour was laughable. It's got to the stage now where bike racing is almost a mainstream sport in Britain. Back in the 80s, my parents never showed the slightest interest in cycling and I was the only person in our house who watched the Tour on telly. Now my parents are both avid viewers of the ITV coverage and get quite excited when it's on. Even if BC haven't been directly involved in the development of the Yates brothers, they may have indirectly influenced their decision to pursue pro cycling as a career.
Hugh Carthy, however, seems more the Robert Millar type and would probably have got into cycling anyway.
As does Froome, for that matter, though he probably wouldn't have got where he is today without the involvement of British Cycling in pushing his career along.