Picking your first assumption (I didn't know that the state killed people on assumptions) apart. So this drunk middle aged man who has had a bit too much to drink goes home and starts to think of raping and killing a little girl and he waits up till after 3AM to do his dirty deed? LOL.....no way, being a middle aged man who ocassionally has a bit too much to drink, I can tell you that once he gets home he goes to bed and sleeps till dawn.
But you see, I don't think Westerfield got home, went to bed, and slept to dawn. I think he left the bar, went back to his neighborhood to wait outside, watching the van Dam house. And according to his former girlfriend, Westerfield has a history of that behavior. She was caught in a misstatement about how she found him waiting outside her home, for her to get home from a date, after they had broken up. She also testified as to why she broke up with Westerfield. She said he's a mean drunk...not a sleepy one.