Yes, they are proficient with the weapon listed. No, that does not limit them to ONLY proficiency with that weapon. It just means that the book isn't going to give them a weapon that they aren't proficient with.
Well there is no rule saying they are proficient with all simple weapons either.
They also don't get proficiency with improvised weaopons, and niether do PCs. I think a commoner would be a lot better at swinging a chair than effectively employing a dagger.
Your argument would mean that an NPC knight would not be proficient with maces, morning stars, daggers, long swords, short swords, and on and on. What knight have you ever heard of who is only proficient with greatswords and heavy crossbows?
This is exactly true RAW and I would not have them use their proficiency bonus with a greatsword or heavy crossbow and I don't use in it the game I DM if I am using a statblock RAW. If I don't like it I will make up my own statblock.
Also as an aside, RAW a knight would have disadvantage using a heavy crossbow.
Edit: Plus you are cherry picking from the MM in any case.
I am using the commoner statblock. To the best of my knowlege there is only one commoner statblock in the monster manual.
"You can equip monsters with additional gear and trinkets however you like, using the equipment chapter of the Player's Handbook for inspiration"
Sure. But that is not the standard commoner.
I think too if you are trying to make a point about how weak a Dragon is when facing a horde of commoners, giving them any weapon not in their statblock is a bit disingenuous, let alone giving them proficiency with said weapon. That is cherry picking IMO.
What about commoners with Oathbows and arrows of Dragonslaying .... or modern firearms? You can equip them with what you want as you said, and you can make them proficient in that, but the default commoner is not.
"Assume that a creature is proficient with its armor, weapons, and tools. If you swap them out, you decide whether the creature is proficient with its new equipment."
So since the PHB says commoners are proficient with simple weapons, crossbows work out juuuuust fine.
It does not say they are proficient with them. Go reread your quote. It says commoners use them and PCs are proficient with them.
Commoners use improvised weapons too, and they are a lot easier for someone to use effectively than dagger, and it is safe to say commoners are not proficient in improvised weapons since this requires a feat even on the part of a PC.
Keep in mind lack of proficiency does not stop NPCs from using other weapons, they just don't get their proficiency bonus with it, which makes complete sense to me, especially considering the level of expertise needed to employ some simple weapons.
We had this actually happen recently with a prisoner freed in a dungeon. It was a gladiator and he did not have proficiency with the weapons they took off the bad guys. He still used them of course.
There are lots of dumb rules.
If we are talking about what makes sense - Giving commoners who rarely ever train with a weapon proficiency with javelins, daggers, light crossbows or slings makes no sense given the extensive training required to use one of those weapons effectively IRL. Giving them proficiency in clubs, spears, light hammers and sickles makes sense.