People die or suffer serious harm in hospitals all the time. This often happens during sleep, and in many cases it could have been prevented if the patient had been checked on more frequently. It is much easier to confirm that the patient is ok if they are awake. When the nurse softly asks "do you feel ok?" when drawing blood in the night, it is not just meant as soothing, but just as much to check if further treatme…
If they wake you up while they're checking something, obviously they are likely to ask is you need anything. But that is not the topic of the discussion.
Also, its usually phlebotomist, not nurses, who are drawing blood at night.