Military service has been a tradition among many noble families of Europe, and I don't see why he shouldn't do it. After all, he is "the spare", and William the "heir", to use M:TW terminology.

After all, even in the days of the Hohenzollern Reich, we in Germany had a long-standing tradition of making our nobles fight in the danger zone - stray artillery shells from miles away are still fatal.

Spoiler Alert, click show to read: 
That's actually not completely fair - von Bismarck's son fought, William I was a soldier-king first and foremost, and I could go on. Such is life.