I think the next step beyond SSTs has to be suborbital craft, that can boost themselves outside of the upper atmosphere in an elliptical path that takes them down to Earth in a long glidepath right towards the intended target… ah, destination.
Yes, that is how ICBMs work. Hopefully, we’ll be able to de-weaponize the concept enough to make it palatable to the upper-class business traveler. That would involve trading solid fuel for liquid, and, indeed, dropping the whole idea of a missile in favor of something that isn’t an aircraft but can still take off and then land safely multiple times without needing to throw parts of itself away each time. Also, a vertical launch will not be acceptable. Brief freefall might be acceptable, but only if it is controlled and the hosts offer Dramamine the same way they offer pretzels now.
Anyway, SSTs in the mold of the Concorde are, for all I can see, obsolete.