It's missing a tuner card, so you can't connect cable to it. And never mind the fact that even if they did add a basic one, people would expect HD cable/satellite to be supported as well.
A game console will never make a good DVR. You don't want it recording a show at the same time it is streaming stuff to the hard drive to reduce load times in a game, for example.
In addition, recording takes SOME processing power - console developers expects 100% of the CPU & GPU. Once you start adding multifunctionality like DVR, then console developers will hate having to take that into account.