Most spaceplanes are aerodynamically just hypersonic airplanes. The tailless delta wing with directional stabilising fins on the tips is an optimal solution, especially if you do not want a fin on the fuselage. Directional stability can be elusive and highly non-linear, so types designed before the days of high-speed digital control systems often resorted to extra-large surfaces.
During re-entry a spaceplane cannot nosedive or it would overheat and melt or tear itself to bits. It has to kind of pancake down on its underside, keeping just enough forward speed to maintain aerodynamic control (An orbital craft needs hi-tech heat insulation even for this but for suborbital craft it is unlikely to be needed). The safe angle for this manoeuvre is really quite small with little room for error, just a few degrees either way. It was an acceptable risk for the Space Shuttle but may not be for commercial passenger flights.
SpaceShipOne and Two are a unique solution to the problem of safe re-entry. The tail configuration is known as the outboard tail or outboard horizontal stabilizer (OHS). It has been studied from time to time but never really flown (a German research prototype was built in WWII but it is unclear whether it ever flew). It was adopted for the SpaceShip series for the obvious reason that it gets the stabilizer out of the way of the rocket exhaust. It also eased the mechanical solution to their other big aerodynamic innovation, the variable-geometry "weathercock" tail. By swinging the tail up for re-entry, it stabilises the spaceplane as it pancakes back down, hugely increasing the safe zone and making re-entry almost trivially safe.
Passengers returning from actual orbit present a far greater challenge, as yet unsolved.