Many bodies, companies and individuals have a vested interest in increasing the popularity of the sport. They would all care. On a personal level, I find the relentless march to world domination that most sports' governing bodies seem to see as their remit a bit weird, but on the other hand, I would welcome more strength in depth within the game, so I care too.
I would say that it's very un-rugby to worry about this. My perception is that 95% of PR and marketing within the game is atrocious. Having an awareness of how the game is perceived within the wider sporting community would be a step in the right direction towards managing and altering that perception for the better.