Absolutely, true, but: For many of the folks in the UK, the royal family is the biggest symbol for Britain. The loss of such a symbol is devastating...look at the death of Princess Diana, for an example. Loss of a serving royal in combat would make it very difficult to maintain public support for a war in Afghanistan. The Brits have shed a lot of blood there, in the past 170 years....
British royals have three basic rights: The right to be informed, the right to advise, and the right to be seen. With just that, they have a lot of power, whether formal or not. It should be noted that British soldiers and airmen, upon joining the service, swear an oath of allegiance to the Queen, not to the Prime Minister or Parliament. If the Queen said publicly, "Bring our troops home," the troops may not directly obey, but public opinion may result in their return.
Agree with the wish that our politicians had some "skin" in the results of military policy decisions. A few do, of course. Sadly, though, we've gone hard-over in the other direction, in being a combat veteran is now a liability when going for high office.
Ron Wanttaja