The scientific method has usually worked by either coming up with theories and testing them; or by measuring things we thought we knew and finding new explanations when those turn out to be false.
What has not really worked too often has been coming up with mathematical models out of thin air, fitting them to all of the current data, extrapolating them to things we haven't been able to observe yet, and then building those things to check if they also worked.
That is why research into astronomical objects to ever greater precision is a promising candidate: we know what we expect to find if our current theories are correct, we know of real problems with our theories, and we can come up with new theories that predict such and such structures that should be visible in precisely such and such conditions.
This is the exact same model of how physics advanced from Tycho Brahe to Newton - people had models of the motions of the stars, they collected data to confirm those models, and found problems that they couldn't explain. Then Newton came along and found a mathematical model that, for the first time, explained those observations, and even reconciled them with other observations on the ground. We then spent a lot of time testing Newton's theories and didn't find any holes for a few hundred years.
Along came electromagnetism, the study of its dynamics, and the discovery of the speed of light problem, which couldn't be explained - requiring a new model that could actually explain everything we knew + the new data, and so on.
But this is the story of early to mid 20th century physics! General relativity, the initial quantum mechanical theories, Dirac’s equation and anti-particles, neutrinos were all the product of this process of adding mathematical conveniences and extrapolating to things that turned out to be real. You can argue that more recent efforts in this direction have been much less successful than those were, but I think you have to turn a completely blind eye to the history of modern physics to claim that method “has not really worked too often”.
I'm less well versed about the other subjects you mention, but there were several unsolved problems in physics at that time that absolutely required new theories (the photoelectric effect VS the wave behavior of light, black body radiation, the need to reconcile quantum mechanics with special relativity). In all of these cases, we had unexplained data or inconsistencies between theories.
By contrast, most of the theories that could be tested with a new collider are not solving anything - they are just theories about things that might exist, but could very well not exist at all. There is no hope of gaining insights into the measurement problem or quantum gravity at the next collider.
Even the theories of dark matter that could be tested are still too early to be worth a 20b bet. There are too many equally plausible theories of dark matter to say any one of them is promising enough to be worth that amount of money. And even ruling one of them out will not have a major effect on the field. It's not like it would rule out string theory, for example.
That's happened to many people (Hossenfelder included?) but it's now happening to the community and no one likes it. But given that is how science as an institution operates they shouldn't be surprised.
Here's a thought experiment. Would there be a bid for a new 100Tev machine if super symmetry had been confirmed at LHC? My bet is :for sure. And the key argument would be "we told you that we were good last time, so you have to back us this time"
Something had to happen at that scale, the Higgs wasn't guaranteed. Sabine gets experimental physics backwards because no one planned the LHC to confirm the Higgs, but to know whether the Higgs existed and if it didn't what did instead. My money was mostly on it not showing up; many physicists were convinced it wouldn't, then it was there but we couldn't know beforehand.
There's a scientific case for making precision measurements of it, as was done with the electroweak bosons for very good reasons that she dismisses without showing any kind of understanding about the research she wants to shut off.
Regardless, the point stands: we knew that something is missing from the Standard model, and we knew that it must exist in a very precise range of energy. If it didn't exist there, it could have called into question the whole SM.
In contrast, we don't know that there must be some kind of dark matter at the 100TeV scale. We know that one particular type that we have thought about could exist, but we have other candidates as well, and there are ways that the 100TeV prediction could also be moved to higher energy levels.
Meanwhile, we don't even know if dark matter is a kind of matter or a modification of the force of gravity or a problem with approximations of Einstein's equations used in practice etc.
I'm not sure we're done with composite models. There are more exotic alternatives and then the fact remains that neutrino masses aren't in the SM.
I consider pretty hopeless to keep thinking that you can modify GR like plasticine in all the instances in which putting amounts of matter that doesn't radiate works (maybe it works because it's there and its effects on other stuff is how you "see" it). It has the appeal of making some people feel like they can call a whole profession or several a bunch of crooks, and that's pretty much what it has going for it outside of the scientists working in earnest on it.