"Just use wifi for headphones"

and

"One less thing to worry about"

These are not compatible statements. :)

WiFi is nowhere near as low energy as Bluetooth is.

If you think wireless headphones are insecure today, I very much doubt connecting them directly to the internet would improve the situation.

and enjoy your precious 1 hour of listening time.

The whole tcp/ip, wifi stack is at least a magnitude more complex than bluetooth one, and the wifi radio generally consumes more power.

Qualcomm kind of does this with their XPAN extension, sends the audio over local network. I believe it's mostly a proprietary solution though, so I haven't seen any serious attempts to re-implement it yet.

That exists, using proprietary 2.4ghz dongles usually, but they’re much higher power draw.