The reason so many London derbies are shown on TV is because there are so many of them. It's not rocket science.
The issue of whether they are boring because they are played by London teams is a nonsense in the modern age. No football team is a representative of its community on the pitch any more, particularly in the Premier League. All matches, no matter who they are between are simply contests between teams of foreigners played out on English soil.
A London derby is as likely to be exciting / boring as a match between two Manchester / Merseyside /Yorkshire / North East clubs or anywhere else for that matter.
Northerners often claim to be more "passionate" (oh, please) about football but they're not. They just like to claim they are.
But talking about the volume of London teams, it's quite telling that London is capable of financially supporting so many clubs. Other cities have tried to have large numbers of clubs but couldn't do it. Take Sheffield for instance: As well as United and Wednesday clubs like Sheffield, Sheffield Albion, Sheffield Heeley and Sheffield Providence all came and went for lack of support. Yorkshire clubs are generally of lower league standard both on the pitch and at the turnstiles so the claim that the north is some sort of hotbed (where did that silly phrase come from anyway..??) of football is a myth.
So don't knock London for having the clubs who can hack it at the highest level and the fanbase to maintain them. Get up amongst the big boys and the cameras will turn up soon enough.