It's an unrealistic rule. Life isn't like a cowboy film (which is a crying shame IMO).
Have you ever tried smashing a bottle in that fashion? It's really difficult.
Granted, since real glass isn't the sugar-glass used in movies. And bottles are generally designed for rough use without breaking. But I've seen a fair few beer bottles break leaving a good handle with a small guard ringed by jagged edges. Never thought to do a percentage comparison which might help for a quick rule though. So I agree, to a point...
If it does break it will usually break at the neck, leaving the wielder with a small piece of glass in their hand.
Yep, which fits the Dagger -1 in my mind. So that part isn't that unrealistic.
IMO the bottle would most likely remain a club throughout the fight, with a smallish chance of it failing & becoming useless.
So all you really need is a quick and dirty house rule for if the bottle actually breaks. Though if it fails I'd still say you have a sharp weapon in hand most of the time. Not a good one, but far from useless. Even a small piece of broken glass is a weapon in a melee.
Your skull is quite a bit weaker than the average bottle. Anyone who is hit round the head by a bottle with enough force to break it is likely to be dead or very nearly so.
But the game doesn't resolve hits to specific body parts or specific force to them. It's abstracted. Sometimes that "hit" with the bottle will be a glancing blow to the arm (no break, little damage done). Sometimes it will be a deadly blow to the head (no break, damage resulting in stats to zero). And even the misses could break the bottle (wild swing misses the target and smashes the bar).
It's a game and as rule it works ok, but refined a little per your reality check would make it better imo.
I just can't recall the last time* anybody resorted to Brawling skill where they weren't just using hands and feet. And as noted previously, any fight in a bar or elsewhere generally escalates quickly to real weapons.
* might have been done in an online Traveller game I was in a while back, there was a bar fight, and someone might have tried a chair...