The incompatibility of shift work with a homeless shelter was very surprising. Wouldn't 'hot racking' like on a submarine increase the capacity of the shelter and the homeless could get shift jobs that might be easier to find.
Shelters can also use the time during the day to clean up and do any maintenance that you couldn't really do with people trying to sleep. Also if the workers are volunteers it'll be way easier to get enough during the evening than any other time.
They're in it for the prestige. Showing people that you care about the homeless is a sign of moral virtue, regardless of whether you're actually trying to help.
Consider what the jealous groupies sing about Captain Hammer's girlfriend in Dr. Horrible's Singalong Blog:
So they say he saved her life
They say she works with the homeless, and doesn't eat meat
We have a problem with her!
Why equate working with the homeless with not eating meat? Those are both displays of feminine caring.