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Tying the buying power of its citizens to the computational ability to hash numbers really quickly?

I'm not sure how those two things are related. Mining is an entirely optional activity for users of Bitcoin, and indeed, the vast majority of users never have nor ever will mine.

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They do not have to do it to be influenced by it. The exchange rate of BTC is always going to be tied to mining activity, and hence hashing speeds.

You've got it reversed. Mining activity will be tied to the exchange rate. Total mining rewards (denominated in BTC) are constant no matter how many miners there are, so the higher the exchange rate, the more people mine as it becomes profitable for them to do so. Mining is a zero sum game.

In addition to what tlrobinson said, you only need a small threshold of hash power for a cryptocurrency to function. More hash power reduces susceptibility to 51% attacks for those coins that are at risk for it (including Bitcoin), but it does not impact the functionality of the coin in any practical way.

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