I was working as a video/audio engineer for a bit and for Bluetooth especially the latency is insane. For some devices it was around half a second. I don't think I have seen two seconds though. The main thing was that we would need to stream the audio first, wait for the latency duration, then start showing video frames. If you press pause, the audio would stop after that much time. I haven't checked if some devices allowed sending of start/stop commands through less latency methods though. My job was mainly concerned with playback.