I’m just saying if I was a doctor who villain… I’d win.
No, you wouldn’t.
The Doctor would not put himself near to you in any circumstance in which you would shoot instantly.
Or A Good Man Goes to War:
“Three minutes, forty seconds… AMELIA POND! Get your coat.”
And it’s frequently even enough to get his adversaries to rethink their approach altogether, because well, he has beaten them time and again, so when he’s just standing there, proudly announcing he’s got nothing up his sleeve, they’re going to think, he’s definitely got something up his sleeve. Case in point.
Yes, and his approach to espionage/counter espionage is to drive an Aston Martin up to whatever upscale venue his target is currently residing at, introduce himself (usually as Bond James Bond) and then antagonize him by beating him at baccarat and hitting on his girlfriend.
There was a very amusing piece of Marvel Comics fan fiction somewhere, where Galactus rolls up to the Earth, threatens to eat it, and then looks at the gathering of superheroes. He asks where Reed Richards is. When it is explained that Richards is off somewhere else, Galactus says, oh well, never mind, I’ll come back later.
Perhaps the Daleks secretly love the Doctor. The entire interaction between the Doctor and the Daleks is a slow burn, unrequited romance.
Because he immediately starts taking command and sounds authoritative. After only a few sentences, it’s clear he knows what he’s doing and probably understands the situation better than anyone else on the bridge.
People respect competence.
Yes I can’t tell you how many times in Iraq some Al Queda type would walk into the command post and start issuing orders, I just loved taking orders so much it never occurred to me to shoot him.
You don’t shoot unarmed people just because they’re in the wrong location. At most, you detain them (which does happen to the Doctor). And especially if they clearly will be useful to you.
But go ahead and ignore expert advice. That’s the way to survive a dangerous situation.
Where’s the comedy reel where they just keep shooting and he keeps popping up as different actors? 
It’s in “Curse of the Fatal Death” actually, which is probably on Youtube somewhere (check out the last 10 minutes or so).
That’s why the episode called “Midnight” is so good - it puts the Doctor in a situation where looking competent makes him the chief suspect among a crowd of rightly terrified people with access to an airlock.
In a lot of situations, what people want is someone to walk in and take charge. The Doctor does it and sounds like he knows what he’s doing. Doesn’t mean no one questions him and we still get the occasional “But I’m in charge here!”
God knows I’ve seen it happen enough, and done it myself, in business situations as well as in gatherings, gaming, volunteer work, etc.
Of course, in the latter couple of situations, you’re more likely to hear “Who put YOU in charge?” (Answer: If you had wanted to be in charge, you would have been talking before I was.)
If you kill him off now, he won’t have a future self.
Many years ago, a tabletop role-playing game magazine called Different Worlds ran an article on how to adapt comic book superheroes to a game campaign. The writer noted that the Justice League includes several superintelligent aliens, scientists, and expert tacticians; but when trouble strikes, they all ask “Well, Batman, what do we do now?” He concluded, “Obviously, Batman has the power of Automatic Area-Effect Intelligence Drain.”
True, and that ability’s sometimes boosted by a gimmick: Psychic paper that looks exactly like what the viewer wants to see. It’s easier to take charge when you’ve got an inspector’s licence, or police ID, or… 
Exactly what someone with a primitive understanding of time travel would say As long as his future self keeps you from killing him, he’s not dead, so his future self exists. And he’s been shown messing around with his own timeline, even at a fixed point in time, to make sure that an apparent or risked death doesn’t happen. You might think you’re killing him, but you’re actually just activating a transmat beam, or killing a robot that looks like him, or…
The slightly psychic paper was invented for the revived series, and works well to speed up the storytelling. On the old show, the Doctor would often spend an episode or two being locked up and/or disbelieved by the authority figures, until they finally figured out that they needed his help.
That’s fine if you’ve got six or seven episodes to work with, and need all the filler you can get. When you’re doing a show where each episode is only 45 or 50 minutes, apart from the occasional two-parter, you’ve got to pick up the pace. Hence the psychic paper, to cut through all that “But who are you, and why should we listen to you?” time-wasting.
But even on the old show, the Doctor pretty much always operated simply by assuming command, and since he was the protagonist, it always worked. See the classic Tom Baker story, “The Horror of Fang Rock”:
Lord Palmerdale: Are you in charge here?
The Doctor: No, but I’m full of ideas!
But the Doctor operates in different timelines, doesn’t he? You may kill him off so he has no future in Timeline A, but not Timelines B through Z.
I was going to say that it’s a badly written children’s show that has survived this long and become an institution because Britain is just small enough for Doctor Who to get away with it. But your answer actually works pretty well.