Most likely it's aspirational, something to market to investors and potential employees.
Neither the investors nor the potential employees strike me as gullible. By the way, the $100 ticket price target was not for the first aircraft, see [1]:
> The four hour, $100 dream is Boom’s long-term aim, two or three generations of aircraft down the line.
[1] https://www.cnn.com/travel/article/boom-supersonic-four-hour...You've forgotten to cancel the denominator. If you use the drag relation of speed to power, you're multiplying by time, but the time is reduced by the speed. It would be more straightforward to use the F ~ v^2 relation between speed and force. So going 4x as fast for the same distance would require 16x the fuel, while going 4x as fast for the same time would require 64x the fuel. But the latter would obviously never happen in practice as you'd circumnavigate the Earth.
The supersonic plane would have advantages over the rocket approach though. Rockers require long, inconvenient transfers to offshore launch facilities. (But would have the selling point of a microgravity transit.)
The terminal deceleration on an ICBM trajectory would be lethal. Ballistic passenger transport at global distances has to be almost orbital so the entry is sufficiently shallow.
But judging by "in four hours" I'm guessing he's imagining something somewhere in between those two extremes. High enough to substantially reduce drag, low enough that you don't need to approach orbital velocity to maintain altitude.
My comment was not a support of that argument, but a clarification that simply being in space does not automatically mean no aerodynamic forces. I'm also not saying L/D increases, actually the opposite happens at higher speeds and altitudes.