Does lift-to-drag ratio asymptote to 4 (or 6) at high Mach numbers?
My source is STUDIES OF HIGH LIFT/DRAG RATIO HYPERSONIC CONFIGURATIONS by John V. Becker, to be found online here. It is from 1964, so more than 50 years old, but since a lot of research had been performed already before that date, it might still be relevant.
In short: It depends. On thickness ratio and Reynolds number, for example, as can be seen in this plot for flat plates from the above linked report:

Note the grey areas noting the maximum for glide rsp. reentry vehicles. Their performance is roughly half as good as that of a flat plate.
Most of the report uses the volumetric efficiency parameter $\frac{V^⅔}{S}$ for comparisons. This is the volume $V$ to the power of ⅔ divided by the reference area $S$. Below is a carpet plot for a variety of wedge shapes, valid for Mach 6.8 (same source as above).

An infinitely thin wing will achieve an L/D of 6.5, irrespective of its leading edge sweep, and a more realistic t/c of 0.09 will not get above an L/D of 5.5 at 85° sweep, dropping below 5 for 70° sweep.
It seems the Küchemann approximation holds up well for single-digit Mach numbers but becomes too optimistic above this speed. And impact theory alone is not sufficient to predict L/D with any confidence.
The plot below explains why the Shuttle is a low wing configuration: Above Mach 10 it is cleary advantageous to put the flat side on the bottom:

The index FB represents the flat bottom version of the vehicle.