This is not an issue of Bluetooth itself. Some audio devices include too large caches (because in the early days not having interrupted audio was a bigger deal than having video and audio synchronized), but you get Bluetooth audio devices just using the default SBC codec that don't have any noticeable delay. Using codecs like aptx adaptive fully solves the problem.

The reason you don't see BT gaming headsets is not latency, it's Bluetooth missing a proper mode to submit audio in high quality bidirectionally. Long story short: when you got high quality sound on your headphones, the mic of your headset is not in use. When the mic is in use, the quality of the headphones is reduced to basically telephone call quality.

There have been technologies trying to work around that, most important would probably be faststream, but it never really caught on. It's pretty
obscure still, you have to take care that all the devices and software you want to use support it, so I guess it's just easier and cheaper to get a dedicated wireless gaming headset with dedicated USB dongle.

At least since BT 5.0 I read stories that BT will be able to support gaming headsets aaaaany day now but well, nothing for now.

and it's proprietary, so less adoption

I sometimes control a high end camera through my phone. For basic controls it connects via Bluetooth but if you want live-shooting (you see what's being captured on the phone) it switches to WiFi. It's ALWAYS a massive pain in the ass, takes forever to connect, disconnects if the phone screen is off even just a few seconds, etc etc.

I'm not sure it's always the only thing people want. Yes stability is needed, even more when a lot of people are using it.

But currently headsets are heavily missing (very) high quality wireless audio and mic at the same time. Maybe this tech could push towards that.