It's possible that it may make sense to establish a few business class only very fast point-to-point routes. But that also really depends on the vehicle taking people through space. There are a number of problems:
1. Currently, spacecraft are only licensed for experimental travel. Everyone signs an informed consent waiver and basically disclaims all liability. And the FAA is forbidden to regulate for passenger safety by congress (and has been for quite a long time) - they can only regulate for the safety of the general public.
This would have to be changed before any serious commercial spacecraft went into service
2. It's not clear that any spacecraft has the economics to pull this off. Maybe Starship can do it. But it's pretty far from clear that they can.
3. Spacecraft are orders of magnitude less safe than commercial aviation. Do you know the saying "regulations are written in blood"? If this starts happening, there'll be a lot of new regulations that happen over time.
And maybe that'll happen anyhow - I think that space tourism will certainly be a thing that becomes much more popular in the future, and that has the exact same problems (although it's much less readily comparable to commercial aviation).
Seriously. Just have the whole passenger section setup like cargo pallets and wheel them in and out of the plane. Why bother walking up and down a narrow aisle? Just have a "passenger marshalling facility" away from the airport, have the interior section in parts there, have everyone comfortably load up, put that on a bus, wheel that straight to the plane, then load them in like large scale cargo through a huge side door.
Lock them down and send them wherever. Do the same in reverse at the destination.
https://www.atlasobscura.com/places/dulles-airport-mobile-lo...
And yes, evacuation issues kill the idea.
Reading this unlocked memories of the (after googling it) September 2005 National Geographic Kids magazine, which was centered around future life in 2035. One of the things in it was exactly this: travel time cut by launching into orbit and flying around the planet to cut travel time down to ~1h.
Rather than trying to take time out of the "middle" of the journey (ie when you're on a plane), we would be better served as a society to take time out of the "ends" (before takeoff and after landing).
But nevertheless I still think it's worthwhile for us as a species to look at ways we can cross the planet faster. I think eventually (maybe in our lifetimes), the idea of taking a flight that takes you into outer space won't be too far fetched. While I don't think the time savings going supersonic will be worth it, I think the savings when going into outer space will, assuming we figure out a economical way to get people up and down from outer space.