Conceptually, yes. Practically, unless you want to suggest that your node does the same volume as coinbase, no one is going to care what you think, unfortunately.

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Anything that became known as "Coinbase Pseudodollars" would lead to a hard fork. Why would anyone, who is using Bitcoin to diversify away from the USD, then stick with the USD fork? A Bitcoin that is US government controlled has no value proposition. It's just eDollars. Fedcoin.