So did you pay attention because vampires can feed on recently killed people just not on long dead bodies as far as i can remember. As logicaly victim can die during the feed and the vampire still can keep feeding.
Also it's not Interview with a Vampire it's TES and there are many vampire settings that vampires can even feed from blood bags: Like "Vampires the Masquerade" which is arguably "the" best vampire setting.
Over the years the whole vampire legend has been generally bent over a desk and given a good seeing to by any number of people.
Fundamentally vampires only feed from the blood of a living person, not a dead one. As has been pointed out previously if you feed off of the blood of a corpse you are not a vampire, at least not for very long.
The "Blood Bag" thing is something that's been brought is simply a device to be used in a plot, for whatever reason. The blood itself is still "dead" and therefore couldn't be used, if one were being entirely accurate.