The idea is to protect lighter weight occupants who are wearing seatbelts; they're not particularly reliable in the case that someone has yanked the seat belts tight on a car seat that is sitting on the seat bottom.
Some quotes from your source:
> Placing a forward-facing child seat in the front seat can be hazardous, even with advanced front airbags that automatically turn the passenger’s front airbag off.
> WARNING Placing a forward-facing child seat in the front seat can result in serious injury or death if the front airbag inflates.
> WARNING Placing a rear-facing child seat in the front seat can result in serious injury or death during a crash.
"The idea is to protect lighter weight occupants who are wearing seatbelts;"
Not exactly. Lighter weight occupants are not supposed to be in the front seat wearing a seatbelt. The same places you're getting the warnings for not placing child seats in the front seat will also tell you not to put children in the front seat.
They try to plug it as a safety thing as a way to protect ignorant consumers from themselves.
This is a lot of fun when you have a big dog that likes to ride in the front seat, or even if you just put a bunch of groceries in the passenger seat, since it also makes the seatbelt alarm go off.
So what's the difference between a front seat without the airbag on and back seat?
My guess is that it's really just automakers CYA so they don't have to treat it as a safety critical system. There's really no reason to have that sensor then.
It is part of a safety system, but the other way around. One of the purposes is to make an annoying dinging sound when the passenger does not put their seat belt on.
Some quotes from your source:
> Placing a forward-facing child seat in the front seat can be hazardous, even with advanced front airbags that automatically turn the passenger’s front airbag off.
> WARNING Placing a forward-facing child seat in the front seat can result in serious injury or death if the front airbag inflates.
> WARNING Placing a rear-facing child seat in the front seat can result in serious injury or death during a crash.