Well, to be fair, there haven't been a lot of opportunities for them to do so. Which is a good thing. Prince Harry flew Apache helicopters in Afghanistan and his uncle Andrew served in the Falklands, both of which were potentially disastrous for the BRF because in Andrew's case, Prince William hadn't been born yet, and I don't think Prince George had been born yet, either. Which means they were the heirs to the heir, at least for a short while.
King Frederik of Denmark has had extensive military training and is a Frogman in the Royal Navy, but if Denmark ever goes to war, do you think he'll be aboard ship somewhere? The days of royalty/monarchs serving in battle are long, long gone.