Why the clock is not neutral

Answer it in your head first.

You wake at two and look at the clock. Why does that one small action tend to cost you the next hour?

Because you do not just read the time, you immediately calculate what is left and what tomorrow will be like. That calculation raises your alertness at the exact moment you need it to fall, and it turns an ordinary night waking, which nearly everybody has, into an hour of being awake. Turning the clock to face the wall removes the trigger rather than requiring you to resist it.