Some of the criticism of your statements on self-defense may stem from the fact that your first scenario is exceedingly unlikely, and the second is a bit of a straw man.
Self defense? At 20 feet an assailant with a knife can reach you in 1.5 seconds. Reaction time of college freshmen expecting a stimulus is .2 seconds, twice that if not anticipating it. That leaves 1.1 seconds to draw, unsafe, aim and fire. The assailant will always have the advantage because they are prepared and no amount of situational awareness can offset that.
Some fallacies here are:
(1) You are postulating an attacker with a knife in his hand 20 feet away who has already begun a lethal lunge by the time you notice him, when in fact that is an exceedingly unlikely scenario;
(2) you are assuming that the response to this far-out scenario from the armed victim would be to stand still and try to speed-draw and drop the attacker on the way in;
(3) there seems to be an underlying implication that the victim would be better off unarmed, when in the scenario you describe an unarmed victim is a lot worse off.
First and foremost, most lethal assaults and other forcible felonies do not open with the attacker running at you like a berserker from 20 feet away trying to kill you. Most involve some warning (your abusive ex is trying to kick in your door, deliberate correlation of strangers' movements with your own, or whatever). Even many murders open with a "just comply and you'll be all right" approach to try to make the victim initially passive. Berserker charges would be really tough for anyone to deal with, but they aren't the likely threat.
Second, the whole point of the Teuller drill is to (a) eliminate complacency and (b) demonstrate why simply standing still is a bad idea. The key response to your imaginary berserker charge is to
get off the fricking X while drawing (run to the side, diagonally forward, circle, whatever), try to position yourself on the opposite side of an obstacle from your attacker, etc., but
open the distance. Fend with the non-drawing arm if you have to, to give you a chance to fight back. You may get cut, but in most knife assaults, it is not the first couple of cuts that are fatal, it is the last couple, and at least a weapon gives the hypothetical victim a fighting chance to stop the attack.
Finally, if some blade-wielding nut
is 20 feet away running at you with the intend of killing you, being unarmed doesn't help you. Having a weapon doesn't offer magic protection, but
not having a weapon in your scenario would really, really suck.
Have a gun in your car for protection? What if that “will work for food” guy suddenly sticks a gun in your face through the window and carjacks you? Opening the glove box, console or reaching under the seat is pretty much out of the question so now the guy has your car and a second gun. It might be possible to defend someone else if you aren’t the target, but SELF defense is exceedingly difficult.
This is a straw-man scenario. If you are in your car in the situation you describe, you are
in the weapon, as you undoubtedly know. A firearm in the car is generally there to transfer to one's person at the destination, or for contingencies that involve the car being disabled. NC's CHL reform was spurred in part by a state legislator who wanted to keep a firearm in his car during long, late-night road trips, and became frustrated trying to navigate NC's byzantine car-carry regulations.
For someone who
does want to keep a firearm in case of carjacking (or for women, attempted abduction, which is always the more serious scenario), the place for that firearm is on one's person with a CHL, not buried somewhere in the car, for ease of access and for retention purposes if you have to bail. But again, the firearm is merely a last-ditch backup in case the primary weapon---the vehicle---cannot be employed to escape or counterattack.