Baby wakes to feed but sleeps while feeding

My baby will wake himself 2/3 hourly to have a feed, sometimes he is alert ( maybe two feeds a day) but the rest he sleeps while he eats. And is awake to be burped ( but he hardly ever burps) and then a nappy change then the other breast.
He has an hour of solid play time then bath in the evening before bed. Then after that most feeds he goes back to sleep for as soon as the milk hits his belly.

Is this okay.
I keep reading that baby should be awake and alert for feeding and I should wake him up if he falls to sleep. But why?
He is having lots of wet nappies and a few dirty ones a day.

A week on he is back to his birth weight. Should I just ignore what I read and stop stressing or may there be something wrong?