While it's true that the devices need to be on to do the recording, I imagine there's also a lot of time when they're idle.
My DVR (Sky+ HD) will go into Standby at 01:00 if it's not in use, and that seems like a sensible option.. most of what I record is broadcast during the regular evening slots, between 19:00 and midnight. Of course, that may not be the case for everyone.
Would I prefer it to go into a Deep Sleep rather than Standby? No, because it's startup times are really frustratingly long.
I guess part of the problem in that case is that age-old problem: I am too impatient to wait to use it. My desire for utter convenience outweighs my desire to save a few quid on my leccy bill.
The generation of random numbers is too important to be left to chance.