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Yeah then it is truly rare.
Maybe a rare hat should come with a bag of loot dropped by a would be bank robber. 1000 sats get deposited into your account from rewards when you find one.
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That takes me back to studying auction theory (that's a good thing). These rare hats are a form of all-pay auction. That type of auction has really complicated equilibria and in practice generates odd behavior.
Relevant to SN, in practice all-pay auctions often generate revenue that is far in excess of the value of the prize.
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for rarity it's a good idea. no colors
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I love the rare hats idea. I'd add that only one person at a time should be able to wear a rare hat. There are a bunch of options there: top post, top comment, biggest zap...