>I'd expect the belt supporting a launch loop to have similar constraints [as space elevators], and the dynamic bending of the belt would raise fatigue concerns.
The reason inertial schemes like the space fountain and the launch loop were created is to overcome those material limitations. Aside from the scale, the engineering and material science of a launch loop is relatively straight forward.
The seminal paper, which discusses rotor fatigue and much more: http://launchloop.com/LaunchLoop%3Faction=AttachFile%26do=ge...
I did a quick read and a search and didnt find any discussion of ribbon fatigue. The issue is that the various stressings on the ribbon thermal, bending, tension, and curving through the 28 km loop over many cycles. In general the mechanical analysis of ribbon strength was unconvincing to me.
Launch loops are interesting. They seem to be even more difficult than tether-based space elevators, which have themselves been unable to work due to material strength:weight constraints on the tether. I'd expect the belt supporting a launch loop to have similar constraints, and the dynamic bending of the belt would raise fatigue concerns.
Agree with your speed estimations and that supersonic or near- speeds have very high drag costs and complicated analysis.