Yes, it should, because people expect wireless headphones to be as safe as wired ones, which have exactly 0% (zero, zlich, nada) chance of spontaneously catching on fire.
Wired headphones are still widely used, made, and sold. This would allow the consumers to make an informed choice, and will give the manufactures of safe devices (wired or wireless) the deserved edge in the market.
Also, consider the comments just from this thread about the risks:
>In the end you're carrying a high energy density power source on your head that would love to just catch fire. Don't they teach kids anything in chemistry these days?
>I mean I’m glad it didn’t happen to me, but a billion people are carrying around billions of Lithium-ion batteries. Those batteries sometimes catch fire because Lithium is highly flammable. It’s gonna happen.
>Nothing is perfectly safe, that is how lithium batteries fail. You should know so you can properly deal with problems.
>Well, at lease EVs are spontaneously catching fire.
>Everyone is aware of the risks, there were a bunch of stories about airplane cell phone fires a few years ago.
>lithium battery fires are really nasty, and that's why he got a chemical burn. LiPF6 is a contact irritant, PF5 it decomposes to is a gas, and also a respiratory irritant, and HF PH5 decomposes in the air is a dangerous poisonous acid. This is what everybody visiting a lithium battery factory is told on safety orientation. In case there is fire in the factory, run, preferably until you are few blocks away.
So, paradoxically, the risks are both negligible and inevitable, something that every consumer should be prepared for because "everyone knows" batteries explode, but no manufacturer should warn about, mitigate, or account for in the design because who'd buy their product then?
I hope you agree that the above is self-contradictory.
Now, ultimately, warnings are not a panacea, but they do work. At the very least, having their product labeled as "unsafe to use in bed" would make the manufacturers invest in research that would result in a better product that doesn't merit such a label.