When we were young, my family lived in a town on the Princess Highway in eastern Victoria. Oops – the Princes Highway, as our parents and teachers had to remind us several times before we got it right. A possessive apostrophe would help, and would also make it clear whether it’s one prince or more princes. I don’t think anyone bothers to ask who the prince or princes were. I had to look it up: it was the Prince of Wales who later became King Edward VIII, then the Duke of Windsor (and who didn’t even travel on it!).
I guess that it was originally labelled the Prince’s Highway, but the apostrophe had been dropped by the time of my childhood. If the apostrophe had been retained, there would be a different problem: road signs do not include the, so they would read Prince’s Highway, possibly giving the impression that it was named after Prince Rogers Nelson (which would make just about as much sense).
I searched online for Princess Highway, and I’m surprised that almost no-one spells it like that. There is a clothing label with that name, and a few questions on travel forums.
(The reason I mention this is that my wife and I spent two days on the south coast of New South Wales, travelling on parts of the Princes Highway (it spans New South Wales, Victoria and South Australia.))