I'm shocked to see so many people think Hamlet is overrated. I even considered it at #1. There are a few things about Hamlet that make it amazingly powerful:
1. It's a massable 2 that provides its own +buy. Fool's Gold and Native Village need some other source of +buy to make them really useful, while Hamlet has it on its own. Hamlet+4 Coppers+Estate buys 2 more hamlets.
2. The ability to quickly infuse a large number of Hamlets into your deck give reliability to a +Cards/+Actions engine even without strong trashing, or even any trashing. And there's no issue of having too many Hamlets, since at worst you can use the extra ones as cantrips. The fact that it's a village, a source of +buy, and reduces/alleviates the need for trashing means it nearly enables engine strategies all on its own. The only thing it needs is a means of increasing handsize, which is a pretty common thing to find anyway.
3. Even if you're building an engine in another way that doesn't require Hamlet as a village, it's still a non-terminal +buy, which is useful in any engine.
I also don't understand why a "support" card can't be a "power" card. What defines a card as "support" anyway? If you're going Smithy+FG, which card is the "support" card?
To me, it doesn't make sense to say Courtyard can create a very strong deck "by itself". It's just that it has negative needs from the kingdom, rather than positive needs. Courtyard BM is good when there is a lack of attacks and extra VP cards in the kingdom, since then it can just speed through to half the points. But this is at least a strong a demand on the kingdom as needing it to contain a handsize-increasing card. So even though the only other cards you need in your deck are treasures, you still have other demands on the kingdom.
In kingdoms where it shows up, Hamlet is very often a key card (whether or not you want to call it a "power" card is up to arbitrary definition of "power", but it's a critical piece to the strongest strategy), and almost always at least a useful card. You can't really say the same for any of the other $2 cards.