Re: @Joseph Lord
I wasn't aware of any digital TVs with P-in-P function. They should have the hardware to quickly swap those screens but perhaps they didn't optimise that path and just use a general change channel method.
MPEG GOP length is one fundamental limit but in the typical case you first need to actually tune to the frequency, start demodulating, access the PAT (been a while I might have the wrong table) that will inform you the PID for the audio and video of the channel you need, listen to those PIDs and pass the data to the video decoder. And I've probably missed several steps as I haven't had my head in the DVB standards for at least 4 years.
Regarding boot time maybe it is possible to do better. I know at Sony significant effort was put in to getting picture up immediately and other functions as quickly as possible. There are a number of applications to get going as quickly as possible including EPG data gathering, network connectivity sequence (DHCP etc.), starting subtitle processing, starting MHEG (or HbbTV or MHP), checking the signalling to identify channel list changes and possibly jumping to the HD version of the current service if signalled.. At some point, possibly later there will be checks for software updates (both from broadcast and Internet), if the tuner is not in use there may a channel scan in the background.
All the video and audio decoding will be in hardware but processing all the DVB tables, setting tuning parameters, controlling the demux is all done in software so the CPU isn't completely idle.
My Sony TV goes from a full off to TV picture in about 6 seconds, channel change is available a few seconds later and input selection shortly after that although access to the full menu isn't really possible until about 30 seconds after switch off and the menu is fully populated (including network services) by a little after 40s. This is on a pre-2011 version of Linux when I'm not certain that it was as optimised for fast booting.
I'm not saying that it can't be done any better but that it is at least considered and there is rather more going on than you might a first think processing DVB video.