There are some, but they're very rare. One example is the BA shuttle between London City and New York - only business. I believe there is a French airline doing a "cheap business" Paris-New York as well.
Qatar operate a small business only A319 from Doha to London once a day, or did when I took it two years ago. I preferred the a350 and 787 flights which are 1-2-1 rather than 2-2, but for a 7 hour day flight it wasnt too bad. It was half empty though, not a great use of a Heathrow slot.
I'm not holding my breath for any of these supersonic jet projects to come to market. But, if they do, I expect the nominally "business" or "first" class seating will be more like domestic business today than typical international business class--as was the case with the Concorde.
That’s Boom’s business plan explicitly. Cut down the flight time to a couple of hours and you don’t need to offer a bed, making the per seat cost comparable.
> One example is the BA shuttle between London City and New York - only business. I believe there is a French airline doing a "cheap business" Paris-New York as well.