Our brains are constantly understimulated. It takes effort to try and raise the level back up. When you first get medicated, it's like someone took a load off your back that you never realised you were carrying.
We also tend to be sleep deprived. It is harder to fall asleep, so the level at which we do requires more exhaustion.
Combine these 2 and the sleep thing makes sense. We are suddenly able to just relax, possibly for the first time. We are also constantly tired. It's not surprising we can fall asleep!
Thirdly, many of us self medicate with caffeine etc. Medication makes us but that back.