But even in boxes with multiple tuners (DVRs) your solution would require tying up at least three tuners (current channel plus one up and down) which would cut down the number of simultaneous recordings that are possible. I doubt many people would like that tradeoff.
However, the biggest issue is that most boxes simply don't have more than one MPEG decoder in them.
Some of the channels I like used to be difficult to tune with my previous cable box, because it would not correctly coordinate tuning with the infrastructure, so I'd have to retune. If I left the box on such a channel and turned it off, the next time I'd use the box the screen would be black.
In the old days all the channels were analog, and used 6MHz each (may vary in your region), and channel changes were much faster.
How do you plan to obtain I-frames without decompressing them?