Because you aren't understanding.
No I understand. Using a weapon (or tool or skill) and being proficient in that weapon, tool or skill are different things and have nothing to do with one another.
You keep going on and on about how commoners use crossbows, which even if true has no bearing at all on proficiency.
The PHB is NOT talking about PCs.
The section you quoted from is from an out of date section of the old PHB labeled and you are taking it out of context.
The sentence you keep quoting does not say commoners are proficient with simple weapons, it says "most people" are and you conveniently left off the sentence proceeeding:
"Your race class or feats can grant you proficiency with weapons or certain categories of weapons"
This is the opening sentence from the paragraph you keep quoting and it makes it explicitly clear who they are talking about - "YOUR" proficiecnes, not a random NPC or commoners or anything else, they are addressing YOU.
Further if we are to say this text applies for all NPC then that means they need a race, feat or class to get proficiency because the paragraph you are qouting makes it clear that is how you get proficiencies. Not by being a commoner and since "most" people have these proficiencies then clearly some don't.
So what is the race, class or feat that gives commoners this proficiency?
It's talking about the entire game, which is why the DMG says the PHB contains the rules to play the ENTIRE GAME. You keep trying to make this about PCs and nowhere does it limit the PHB to PCs.
It is not. It is written in 2nd person.
If you option the 5.5e rules, sure. The 5e rules are just as valid, though.
Except the parts which have been replaced ... and that includes proficiencies by race (and race in general in fact) and therefore that whole paragraph considering the first sentence.
No matter how you twist and shout, you can't avoid that most people(which includes commoners who are in fact most of the people in existence) are proficient with simple weapons.
Most people, even in the out of context way you are using it, means some people don't. It means exactly the opposite of what you claim - that being a person does not automatically give you proficiency.
RAW says that most people, and commoners are in fact most people in existence,
No they are not. The entire definition of person is not even clear.
A commoner is a specific monster, and one of over 500.
It doesn't say most simple weapons, so they are proficient with all of them.
No it doesn't. It does not say commoners are proficient with anything.
Apparently, wizards, sorcerers, and druids are not a part of the "most people."
And commoners aren't either presumably.
How much do you want to bet that if a gladiator subclass ever comes, it will be a subclass of fighter and be proficient in all simple and martial weapons?
Gladiator is already a background in the 2014 PHB - page 131. It provides an unusual weapon like a net or trident as starting gear but does NOT provide proficiency with that weapon. To emphasize my earlier point you get the weapon, you presumably use the weapon every day, but you don't get the proficiency in the weapon .... and any PC can take that background. The proficiencies you get from Gladiator are Acrobatics, Performance and a Disguise Kit.
I am confident a gladiator subclass will not provide proficiency in any class of weapons. If they have proficiency it will be because of the class it is attached to.
It is more likely that it will be a background in the future and if they do that again I expect it it will not offer proficiency in all simple and martial weapons.
This discussions of Gladiators brings up another good point. PCs Gladiators use weapons in their performances every day, but they don't get proficiency in them .... yet commoners automatically do???
The NPC gladiator is a fighter with a gladiator subclass, but built via the NPC stat block rules.
NPCs don't have classes and the only official Gladiator published for PCs to date did not require the Fighter class and did not provide any additional weapon proficiencies.