Not letting a potential threat get close is a good idea in general, but there are those of us for whom that approach won't work well. First, there are people who need to spend significant amounts of time in crowds or conditions where they can't see somebody coming til they're close. Second, there are those of us who see poorly.
My vision is bad; I'm blind in one eye and have no peripheral vision in the remaining eye. (It's bad enough that I quit driving a couple of years ago.) I wouldn't necessarily recognize somebody I knew much farther than 20-30 feet away. (At 30 feet, I don't see faces clearly, although movement and posture often make up for that.) I also wouldn't see the expression on a stranger's face before that stranger got within easy attacking distance.
Because I know that I can't count on spotting a threat coming at me til it's close, I work hard on developing the skills necessary to deal with emergencies at close quarters. I practice shooting at from 10 feet to 10 meters; no point in developing good skills at 50 meters when I would probably not see a threat well enough at that distance to know that it was time to shoot. While my carry gun is concealable, it's on the large side for it (S&W M60 3" revolver), and is holstered in a custom-made leather holster designed to fit that exact gun and model. I can count on being able to draw it quickly (I've practiced quite a bit) and shoot it without huge amounts of recoil throwing me off.
I also have pepper spray clipped to the belt or in a pocket within quick reach. That way, if I'm in a crowd and a threat pops up, I have the option of using something that can slow or distract an attacker without putting his or her life, or that of innocent bystanders, at significant risk.
In the summers, I often open carry because that way, I can have the gun within quick reach and not have to worry about concealing it while wearing shorts and a t-shirt. There are risks associated with open carry; I wouldn't do this in a crowd or around children in most cases. But there are plenty of circumstances when the tradeoff of easy access and comfortable carry is worth the extra vigilance.
Fortunately, being a middle-aged, overweight female, I'm not a threatening figure to most people, and live in a part of the country where open carry is generally accepted. That means I don't usually have to worry about scared or nervous people or freakouts at the sight of <gasp> A GUN.