The latency doesn't come from bluetooth radio part itself (there ARE low latency BT headphones after all).

It comes from the fact that all audio is encoded (usually into SBC or AAC or AptX), transmitted and then decoded in the headphones. And each of those steps has buffers. And those buffers are configured by the manufacturer.

The bigger the buffer, the more stable the audio connection - there's less stuttering, less dropouts. But every buffer in the chain adds latency.

So why can't you have both? You sure can. You just need to somehow find headphones and a PC that doesn't add latency to bluetooth. Sadly that's not something that's usually documented in technical specs.