Loads of people received the Coronation medal - the entire Armed Services, emergency service, most of the Royal Family, Beefeaters, those involved in the ceremony (bizarrely not Chelsea Pensioners though). To get one, you simply had to be alive in a qualifying role on the day.
For Royals, I'm not sure how far down the line they go, but as Mike Tindall got a Coronation Medal, Harry must have qualified.
I can think of no good reason to wear less than your full set at a formal occasion where medals are worn.
Except perhaps for the monarch, who holds oodles and so might opt to wear only the British ones or only the most senior, or if hosting a state banquet for a visiting head of state, any medals/orders bestowed by that state.
But Harry doesn't have so many that space to wear is an issue - 1x campaign medal and 3x jubilee medals, one British order (KCVO) and one foreign order (according to Wiki). Wiki however does not list a Coronation medal for him. If he doesn't have one, then my guess is that he declined it (because it's utterly improbable that he would not be awarded it). Or perhaps he's just not got round to having it mounted yet.