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.