Talk to anyone in law enforcement, a gun is always better than your hands, at any range. Self defense simply isn’t practical for most smaller people. I don’t want a fair fight, I want to live.

I didn't say "hands", I said "close combat". Both of those links are about ranking self-defense tools. One of them is literally from a PI and professional self-defense instructor. Not a cop, but more relevant to the topic of individual self-defense. You seem to think your smaller stature means other weapons will fail but your gun will be a trump card, but once you're in close-combat, firing a gun is just as much a conflict of brawn and martial skill, and the way you have to use a gun makes it easier to control or disarm than a knife with a more limited area of danger. Yeah, if you get that area on exactly the right spot and have the wherewithal to pull the trigger before things move again, you win, but you're likely not that skilled in gun-fu and even if you get off a shot that hits the target it won't disable your attacker.

In close combat guns are too easy to disarm, too hard to use effectively, and with a high likelihood of being used against you. They're fine for home defense, if you expect to be shot at, or have a known danger approach from range, but your example worries were muggings.

You misunderstand the “21 foot rule” that is comparing draw speed to someone sprinting at you reaching you. It has nothing to do with you losing a fight.

Once you're in hand to hand with someone wielding a knife, or who is just physically more powerful than you, you're probably going to lose. The knife fighter doesn't just close to knifing range and trade blows like a video game, they're grabbing your arm and starting a grapple. Fights are chaotic and sometimes the weaker or more poorly armed (for the circumstances of the fight) person wins, but once the distance is closed, a gun is at a disadvantage. Cops, who spend time training for these situations, miss most of their shots from short range, and that's with the advantage of usually being able to start the confrontation with their gun out and ready. Once someone can actually grab the gun/arm of the shooter, it's not a gunfight anymore and most other weapons are superior.

A gun in a melee range fight is still at least as if not more than effective than a knife (there are many examples of people being stabbed but still saving themselves from the assailant).

No one on any of the self-defense sites say this, and the self-defense trainer explicitly says a gun is worse. It just sounds like you have fantasies from movies and explicitly ignore real life experts who don't tell you what you want to hear.