This isn't even an audio thing. With a classic television, you can crank the channel dial and (along with the instant audio output) see a stable frame within 5-20 frames of vsync (so like 300ms or so worst case).
My TV at home can't switch an input (e.g. between two HDMI inputs) faster than about 3-4 seconds. No, I don't know why either. It's actually much worse if the device being switched away from is a Chromecast. Don't know why there either.