A transaction fee of what? To take a fee from a transaction there has to be a transaction to take a fee from, which needs some sort of "coin" that came from somewhere. Somebody has to create a money supply and distribute it somehow. When the network first comes into existence, nobody has any money, so where does it come into being from?

Mining is what generates the coins. And you need mining because otherwise you need some other issuing organism. Without decentralized mining you get a central issuer, and that's untrustworthy and possible to shut down.

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