(Is it even possible to knight Prince Philip anyway, I have to wonder?)
Yes, it would be possible, since a noble's title is bound to the realm which issued it. A prince This And That would be a "regular" human in another country since his princedom is bound to the kingdom of his origin.
A historic excample: August II. "The strong" was Elector of Saxony in the Holy Roman Empire, King of Poland-Lithuana and Lord of Ravenstein (among others). As king of Poland-Lithuana he was his own master, as Elector of Saxony one of the most powerful men in the Holy Roman Empire but was subject to the Emperor and as Lord of Ravenstein he was a subject of the Duke of Palatinate-Neubach.
tl:dr As long as Prince Philip from another realm he can be knighted.
That's the guy!
It *is* possible to Knight Prince Phillip, as long as you reverse a decision made 31 years earlier to eliminate Australian Knights and Dames, and eat an onion while doing do.
What?! Ô_o