It won't change the economics of the current class of aircraft. They will still need to have business class seats to pay for the economy cabin.
You will probably end up with 5 or 6 tiers of service instead:
Supersonic: Business + First
Subsonic: Economy + Eco+ + Business + First
Supersonic First will be a Veblen good that has a high price floor (like $30k). Business for time sensitive business passengers, and it's actually an Economy Plus seat for ~$15k.
It's very hard to resist marketing some service differences, particularly when you have two classes of users with different needs (speed vs. prestige).
The pitch quoted from the post I was responding to essentially said it was going to siphon all the business class fliers from normal flights: "Give those passengers a supersonic plane, cut the flight time in half, and charge the same price." There's no way businesss travellers would choose subsonic travel if supersonice was the same price for half the time.
We agree I think that there wouldn't be a similar price between the sub and supersonic travel options. The economics of running the routes can't work out to a similar price to existing offerings.