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).