As someone who usually is rather critical of string theory I like your post a lot. I could come up with other criticism of string theory that your post does not cover, but you do present some very good points. That being said, I disagree with the following bit:
> For example, you can use string theory to study the structure and behavior of black holes and holography, something called AdS/CFT, an area that has been incredibly successful.
Here, "successful" only means that other (famous) string theorists have found those ideas worth pursuing. Then, other people, in turn, picked up the idea because the former people had praised it and then they, too, would receive praise. (It's almost like what people on Reddit call, pardon my French, a circle jerk.) However, AdS/CFT hasn't produced a single bit of verifiable experimental evidence in the realm of black holes. It's not even clear what AdS/CFT has to do with our (clearly non-AdS!) universe.
Yes, when I say that AdS/CFT is successful, I definitely am not saying that we have a falsifiable prediction for black holes, but I also don't mean that these are simply results that famous physicists like and promote, it's a bit deeper than that.
For many years it was conjectured that gravitation is actually most clearly understood as a two-dimensional theory (people call this the principle of holography). The rationale is that the entropy of a black hole is proportional to its area rather than its volume. Since a black hole is in a very specific sense the object of maximum entropy, that means that the amount of information that we can store in space is not proportional to its volume, but rather the area of the encompassing "sphere". This is super surprising since it suggests that what we perceive as 3d is really just an illusion and that the correct formulation of physics ought to be a 2d theory.
Now, for a long time we didn't have a way to actually write this sort of duality down. We sort of knew one side of the story (gravity with general relativity), but it fails in precisely the domains where we want to investigate it (black holes). String theory, whether you believe it's the true theory of everything or not, is nonetheless a mathematically consistent theory of quantum gravity (in a sense it's at least an existence proof that gravity can consistently be quantized). As such, it's at the very minimum a great arena to analyze these problems carefully. The first explicit construction of the duality between a 3d theory of quantum gravity and a 2d theory without gravity is precisely AdS/CFT. It says that a quantum theory of gravity is AdS space is mathematically and physically equivalent to a 2d theory of a conformal field theory that lives in 2d.
I don't think it's fair to say that AdS/CFT is being studied because famous people like it. It really does have a lot of value if nothing else than as a playground to understand how one could in principle formulate these dualities consistently.
I mostly agree with what you're saying but still, the entire "success story" of AdS/CFT is based on other assumptions about quantum gravity none of which has been tested experimentally. Even black hole entropy itself is, up until now, a purely theoretical construct.
> String theory […] is nonetheless a mathematically consistent theory
I hear this claim being perpetuated a lot but I have yet to see a string theorist give a mathematically rigorous introductory lecture on string theory. Don't get me wrong, I'm not saying there are no mathematically precise results in the realm of string theory but I know enough about functional analysis and the issues surrounding the mathematical underpinnings of quantum field theory (or even quantum mechanics) that I'm not buying your claim and my current view is that some parts of string theory are very rigorous, whereas (most) others are not. (AdS/CFT is one such part which belongs to the latter category.) I'd love to be proven wrong, though, so please feel free to send me papers etc.
Ok, when I say mathematically consistent I don't mean it in an axiomatic sense. In fact, like you point out there is a lot of unanswered questions even within quantum field theory whether or not it's mathematically well defined. In fact, one of the millennium prizes is related to this.
When I say mathematically consistent, I mean it in a looser sense. If we take a step back to before string theory, there was no way to get consistent results from quantum gravitational calculations. The usual tools that we use to renormalize quantum field theories do not work for gravity. This suggests that there's some type of "ultraviolet completion" of general relativity. In other words, the theory of GR ought to come with some implicit energy cutoff beyond which the theory somehow changes. String theory is such a change in that the stringy corrections to GR would only come into effect around the Planck scale. It's by no means necessarily the unique such completion, but as of now it's the only one we know of.
As to your other point, I think it's a good idea to reframe the work done in string theory as (what I used to joke) "theoretical theoretical physics". In other words, it may be the case that string theory is a true theory of nature, but even if it isn't, the theory lets us explore what such consistent theories could look like and how various paradoxes (like the information paradox in black holes) get resolved. These types of insights may point us in a direction of further investigation that may very well fall outside string theory.
In other words, at the very least (and I personally think this is underselling string theory by a lot) string theory is a proof of concept and a very powerful, sophisticated, and rich arena in which we can begin to understand the salient features of quantum gravity. One such example is AdS/CFT.
It's producing results in strongly coupled field theories. You take strong coupled physics, translate it to AdS, solve it and translate it back. Then you get answers for problems like the dynamics of quark-gluon plasma.
Given that there have been exactly zero experiments conducted in laboratories close to black holes, isn't that qualifier kind of a cop-out? Our entire observational knowledge of black holes consists of radiation emitted from the accretion disk (deep in the classical regime), orbits of nearby objects (even farther in the classical regime), and one blurry radio picture (predicted by GR and containing nothing, yet, to our knowledge, outside of GR's predictions.) I guess you could count gravitational waves, but guess what, that's GR too... ;) Given the observational knowledge of today, even a true theory of quantum gravity beamed back from the future would fail to produce verifiable experimental evidence in the realm of black holes.
> Given that there have been exactly zero experiments conducted in laboratories close to black holes, isn't that qualifier kind of a cop-out?
No, I don't think it is. I agree of course that it's hard to test predictions regarding black holes. But I was addressing OP's statement that
> For example, you can use string theory to study the structure and behavior of black holes and holography, something called AdS/CFT, an area that has been incredibly successful.
and I merely intended to express my disagreement with the claim that AdS/CFT has been "incredibly successful". Successful in what way? Measured by what metric? Clearly not by the usual metric that says that experimental evidence is what counts. And on top of all of that AdS isn't even close to the spacetime describing the known universe.
> Given the observational knowledge of today, even a true theory of quantum gravity beamed back from the future would fail to produce verifiable experimental evidence in the realm of black holes.
> For example, you can use string theory to study the structure and behavior of black holes and holography, something called AdS/CFT, an area that has been incredibly successful.
Here, "successful" only means that other (famous) string theorists have found those ideas worth pursuing. Then, other people, in turn, picked up the idea because the former people had praised it and then they, too, would receive praise. (It's almost like what people on Reddit call, pardon my French, a circle jerk.) However, AdS/CFT hasn't produced a single bit of verifiable experimental evidence in the realm of black holes. It's not even clear what AdS/CFT has to do with our (clearly non-AdS!) universe.