Is Batman really a hero?

So I was thinking this morning that since Batman operates heavily at night and even has his signal that is meant for the night sky, why don't the criminals just operate in the daytime. It's not like they have real or other jobs. And obviously only batman can stop them, because the police force only clean up after he's done. But then I thought maybe they do have another job. Since Batman pretty much owns Gotham city maybe they work for Wayne corporation. Maybe all the criminals do as much crime as they can that won't really hurt anyone and then Batman comes in to save everyone. If anyone is behind this it's probably Alfred. I'm sure doesn't do anything all day. The master is never home to make a mess. It's either that or have swing parties everyday while Wayne is away. And then I thought when does Batman sleep. He works during the day and then fights crime all night and like the middle of the night too. Because the moon is always behind him. He should have the biggest bags under his eyes. Either way that is my rant.