I feel like this article does not discuss the real reasons why LHC++ would or would not be a success. It absolutely depends on whether you expect it to provide tangible evidence of new physics; that is, physics beyond the standard model. It's easy to say "high-energy physics has become highly academic and mathematical", but if it provided results there wouldn't be a problem with that. Mathematical beauty has proven unreasonably effective at driving innovation in physics [1], and cutting-edge research being academic is nothing new.
The fundamental problem for high-energy physics seems to be the "tyranny of the standard model", as one of my professors called it. We know that our current model of fundamental particles must be incomplete towards extremely high energies (trillions of TeV), because it conflicts with general relativity. However, almost all experimental results are consistent with the standard model.
There are some barely-significant [2] results from muon spin and W-boson experiments, but the effect sizes are minuscule and and two data-points are in no way enough to guide new theory development.
This leaves theorists with almost no experimental input, so they pursue purely mathematical ideas that are in some way elegant, able to describe the standard model as a low-energy limit, and in some cases include a description of gravity as well. But the more advanced and theoretical the ideas get, the more difficult it gets to make experimental predictions. The ones which predict non-standard-model measurements with current equipment are already ruled out anyway, because we did the measurements and the standard model just keeps getting validated.
So what should we do? We can hope that a larger collider will find new evidence of beyond-standard-model physics, but (as I understand it) there is no concrete reason why there has to be anything interesting in the newly-accessible energy region.
[1] As just one example from particle physics: Gell-Mann's "Eightfold Way", which uses advanced representation theory to describe hadrons and was successful at predicting new particles: https://en.wikipedia.org/wiki/Eightfold_way_(physics)
[2] Note that high-energy physics has an extremely high standard of significance at 5 sigma, so it's not comparable to "barely significant" in the social sciences.