What? I have a couple thousand hours on my PS4 with A Sony PS Gold Bluetooth headset, and it is an absolutely awesome setup. (No affiliation, I just like them. I’m on my second pair over the course of about 5 years.)
Maybe you are used to it? Try watching a series or movie and notice when their lips open and if the sound starts in your ears right away.
That's a problem with bluetooth protocol in general.
https://www.rtings.com/headphones/tests/active-features/late...
It is very noticeable in games and movies. Until they solve that problem first, wired solutions will always be needed.