I agree with your market analysis. Private jets are often referred to as "time machines" given how much time HNW / exec travelers can save. There's a market segment that's willing to pay a high premium for reduced travel time.
Private jets don't go faster. They can just land closer to your destination and make you skip all the annoying airport stuff.
For most of my trips, a huge % of the travel time is outside the actual flight time. Trip to the airport, security, boarding, waiting to take off, and reverse on the other side (with addition of potentially getting a rental car). This can be solved without supersonic solutions (e.g. flying private), but adoption is low for business travel – is it too expensive?
Separately, I wonder if a lot of the demand is also obviated by in-air wifi.