He'll still have to provide ID documentation to get on the plane (and I think also to book the flight, under the TSA Secure Flight program) so in practice the government doesn't lose any information here. It might raise suspicion, but he doesn't gain any anonymity.
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Booking a flight with bitcoin.. Doesn't that seem even more suspect than booking a flight with cash?
He'll still have to provide ID documentation to get on the plane (and I think also to book the flight, under the TSA Secure Flight program) so in practice the government doesn't lose any information here. It might raise suspicion, but he doesn't gain any anonymity.