The idea is certainly valid.
Busemann's original design could not generate lift, but modern variations can. Here are just three recent papers on how it can be done:
Wave drag has two causes, one due to the bulk or form of the plane and the other due to the lift generated.
The Busemann concept can eliminate form shock drag but not that due to lift. Busemann's original geometry eliminated all wave drag and hence also lift. Modern Busemann type designs can create lift, with its associated shockwave, while still eliminating much or all of the form drag, thus achieving considerable improvements in efficiency over conventional designs. They can also allow adequate performance over a range of speeds and angles of attack. The three papers linked explore different ways of achieving all this; some use variable geometry.
But Mach 10 cruise is less likely. We do not yet have the materials or airbreathing engines to achieve even half that for sustained flight. Moreover Mach 10 cruise requires extreme altitudes and it can be more economic to go for a conventionally-winged ballistic/suborbital spaceplane which maintains its cruise segment of the journey in empty space. The acceleration of any airborne vehicle can be limited to a level comfortable for the particular passengers, although varying gee levels can affect the economics.
Whichever approach is taken, to avoid overheating at hypersonic speeds above Mach 5 the fuselage nose would have to be bluff like the Space Shuttle rather than pointed like Concorde.
On engines and fuels, the only airbreathing technologies in the offing for these speeds are the scramjet and the airbreathing rocket (principally SABRE). For different technical reasons, both these are likely to be restricted to hydrogen fuel.