First, I was annoyed that The Doctor is portrayed as somewhat all-powerful for no reason at all. He can threaten his enemies and make appeals with no credentials whatsoever. I kind of understand that scenes where he says that "the Earth is protected" by him are perhaps awe-inspiring to a 50's born nerd who has watched all of the previous 200 episodes, but I really don't get why the aliens he is currently facing won't just incinerate him on the spot. To an outside observer, it simply seems like a lame would-be superhero saving the day by just boasting about it. This is actually repeated twice during the first three episodes.
To be fair, that would be like asking why an old retiring captain would be the one sent to meet with Earth's most persistent enemy for peace talks. (Aka, Star Trek VI.) There's been enough backstory to show that Kirk is Starfleet's most successful and well-known captain, plus sending a well-known enemy of the Klingons to peace talks shows a certain symbolism.
It's the same way with Doctor Who. Even simply counting the televised appearances, he's been around for so long that his exploits have become legend, and anyone reading up on them quickly learns not to underestimate him. It's even well-established that the most feared, genocidal, and intelligent race in the universe is so afraid of him that they only purposely seek confrontation in dire emergencies. Essentially, while it may seem like badass boasts, almost every time I've seen him do it it's A) to someone who knows him already, or B) to someone who has access to information that lets them know he is not to be trifled with.
In short, in the series, it's taken for granted that if it were that easy to just incinerate him on the spot, it would have happened long ago. He's just usually too lucky and clever to let it happen for the most part. ;-)