I made a hundred million TVs boot in half the time.
Digital TV tuning is slow because of compression; when you tune to a stream in progress, you usually can't meaningfully decode it until you receive a I-frame. But I-frames are bigger than motion predicted frames, so it makes sense to only ocassionally send I-frames. Latency: technically unbounded, usually a couple of seconds.
It potentially gets a bit worse if you're on a switched video cable system where your box has to request channels, as now there's a request / response delay. But it shouldn't be too long for local comms... And in theory, the head end could start the stream with an I-frame (otoh, it may not have the processing power to decode/encode).
In theory, a TV with multiple tuners could do predictive decoding to help with channel surfing, but I don't think anybody actually does that.
Some systems already do this. When I change channel on my iptv, it immediately shows static frame (looks like last known iframe) and starts sound, then after up to 2s starts playing video, probably waits for next iframe because you can't start decoding from middle of stream anyway.