Executing Wilhelm would be way out of bounds for the Entente governments. In the last several hundred years, the head of state/monarch losing their head for losing a war had dropped out of favor. Sure sometimes "savage" heads of state in colonial wars got the long drop, but not heads of civilized countries. I mean look at Napoleon and the devastation of the Napoleonic Wars - he got exile (one can argue about was he poisoned at the end or not). The only rulers/monarchs that ended up dead were those who fell to internal revolutions. Executing Wilhelm II would be bad form, and be seen as setting a bad example for the future. Furthermore Germany was a constitutional monarchy, why not execute the political party leaders who voted for war, or the Ludendorff and Hindenburg? Yes, Wilhelm had a lot more power than George, but Germany was not the sort of absolute monarchy that Russia was and even there there were some constitutional forms. If you execute Wilhelm what about the Hapsburg Emperor, and the Ottoman Sultan? The crimes of Japan leading up to and in WWII made the worst things the Germans did in WWI look like misdemeanors. For purely practical reasons Hirohito was let off the hook.
I can see Wilhelm being killed by some sort of revolutionary movement in Germany (whether or not folks like Rosa Luxemburg and Karl Liebknecht kept power), but not by the victorious powers.