The toon Links are like, what, 12-13? They're practically teenagers, so of course they're going to sleep in pretty late. After all, it's only natural.
In MC, that can be explained by how Smithy (I think that was his name) and Link were working all night to finish that sword for the contest winner, so it's natural that Link would sleep in pretty late for that.
In WW, I think he just stayed up late watching the gulls at night and passed out. After all, why else would Link sleep up at the top of a tower where there are no pillows or sheets or anything to make his sleep comfortable as opposed to the bed I think there is at his house?
In PH, he wasn't sleeping at all. He was just extremely bored from Niko's cruddy recap of his adventure (it was pretty inaccurate).
In ST, he was bored to death with Niko's history lesson (poor dude got bored to death by the same guy twice, that has to be tough) after doing what we can probably safely assume to be pulling an all night study lesson on the operation of trains. It's only natural that he can't help it that he fell asleep by Niko's incredibly long history lesson.
And Vincent, you're actually kinda sorta wrong about your statement of Toon Link being asleep at the beginning of each game he's in. FS and FSA exist and in both games, he's not once seen asleep. Then again, they're not often considered part of the main series, but still. They technically count since Toon Link appeared in them.