First off, thanks for writing a card article! We haven't got a ton of these recently. I have a couple things I'd like to contribute to the conversation. Take these with a grain of salt, since I don't own Prince on MF and thus don't have much experience with it in high level 2-player games.
I think the biggest thing about Prince, which isn't emphasized enough here, is the reliability aspect. Silverspawn mentions it in the context of card reliability, but it also has a lot to do with the reliability of your deck as a whole. If you have something like an Alchemist stack that is going to draw your deck all the time, you really have no need for Prince, and it's not worth the huge cost. But if your deck is something like Villages and Smithys with a bunch of treasure, there's a pretty good chance of not getting a Village in your starting hand, which can just kill a turn. In this case, Price might be useful.
In a way, Prince acts like a level 2 City and a restricted double Scheme. That Scheme must be used on the L2 City and a card that your want to play immediately after it. So if you have a deck in which you wouldn't buy a Scheme, you should really think twice about buying a Prince. Prince is still a little better if you're not shuffling that frequently, since it persists forever rather than once per shuffle, but it's still just doing the same kind of thing.
Of course the other part is the L2 City. If there's no villages, and you could really use one, it might be worth buying Prince even in a reliable deck. Say you can reliably draw up most of your deck with Stables or something, but there are 2 terminals you potentially want to play -- usually a +buy and something else (an attack, some big source of money like Coppersmith, or maybe another +buy). Having just one extra action can be a big deal here. I'm sure you've experienced this with Necropolis allowing for it, but Prince can do the same thing in non-Shelters games, albeit at a very high cost. But potentially this is occasionally worth it, for example in the Stables/Coppersmith/terminal +buy example.