While you are canabalizing some of your own 1st class passengers, the first airline to get a supersonic route going will also take first class passengers from other airlines.
You mean the third airline? This has already been tried before, and the financials didn't work out the first time. Maybe everything has changed, but who really knows.
And frankly, I'm hoping for failure. Some of these new super-sonic companies are trying to get approval for continental routes, saying that the boom is only as loud a car door. Like a car door slamming shut for 3000 miles is no big deal. The super-wealthy have enough toys to inconvenience the rest of us and destroy the climate; they can keep hanging out in first class, or on their private, subsonic jets.
When I read the headline I was quite confused at first, a big why why why? Then it came to me, it's a business bet on wealth concentration. Conventional first will always be far more comfortable, private far more convenient, but supersonic easily outdoes them both in bragging rights. And think of the networking opportunities when (if?) passengers are almost as packed as in coach despite paying a huge entry fee!
And the environmental aspect won't feel too bad actually: if you are traveling first you produce x times as much CO2 for your trip as others (how many more could they take aboard if that are was as densely packed as regular?), only because you are, well, too soft to sit out a few hours. But if the CO2 happens because supersonic, you get something very real in return. Time! Who could blame you?
Also, far higher climate impacts, which is what concerns me the most. Lets just be happy with crossing an entire ocean in 6 hours.