That's a very good point, CounterBlunder, and I should have highlighted that as well. It is definitely fairly common for cognitive science researchers to never work with or make use of ACT-R. It's a sub-community within the cognitive science community. The research program has continued past the 90's, and there's probably around 100 or so researchers actively using it on a regular basis, but the cognitive science community is much larger than that, so your experience is pretty common.
As for whether ACT-R is "actually amazing and people have been silly to drop it", well, I definitely don't think that everyone should be making use of it, but I do think more people should be aware of its advantages, and the biggest reason for me is exactly what you point out about "fitting human reaction times" not being impressive. You're completely right that that's a basic feature of many, many models. But the key difference here is that ACT-R uses the same components and same math to fit human reaction times (and error patterns) across many different tasks. That is, instead of making a new model for a new task, ACT-R tries to use the same components, with the same parameter settings, but with perhaps a different set of background knowledge. The big advantage here is that it starts getting away from the over-fitting problem: when dealing with comparisons to human data, we normally have relatively few data points to compare to. And a cognitive model is going to, almost by definition, be fairly complex. So if we only fit to the data available for one task, the worry is that we're going to have so many free parameters in our model that we can fit anything we like. And there's also a worry that if I'm developing a cognitive model for one particular task, I might invent some custom component as part of my model that's really highly specialized and would only ever get used in that one task, which is a bit worrying if I'm aiming for a general cognitive theory. One way around these problems is to find components and parameter settings that works across many different tasks. And right now, the ACT-R community is the biggest cognitive modelling community where there are many different researchers using the same components to do many different tasks.
(Note: by "same components in different tasks" I'm meaning something a lot more specific than something like "use a neural network". In neural network terms, I'm more meaning something like "train up a neural network on this particular data X and then use that same trained neural network as a component in many different tasks". After all, people very quickly change tasks and can re-purpose their existing neural networks to do new tasks extremely quickly. This hasn't been common in neural networks until the recent advent of things like GPT-3. And, personally, I think GPT-3 would make an excellent module to be added to ACT-R, but that's a whole other discussion.)
As for the paper you linked to, I really like that paper (and I'm even cited in it -- yay!), but I don't think it gives an overview of overarching theories of human cognition. Instead, I think it gives a wonderful list of tasks and situations where we're going to need some pretty complicated components to perform these different tasks, and it gives a great set of suggestions as to what some of those components might be. But there's no overarching theory of how we might combine those components together and make them work together and flexibly use them for doing different tasks. And that, to me, is what ACT-R provides an example of. I definitely don't think ACT-R is the perfect, final solution, but it at least shows an example of what it would be like to coordinate components like that, and applies that to a wider variety of tasks than any particular system discussed in that paper. But lots of the tasks in that paper are also things that are incredibly far away from anything that ACT-R has been applied to, so I'm quite sure that ACT-R will need to change a lot to be expanded to include these sorts of new components needed for these new tasks. Still, it makes a good baseline for what it would take to have a flexible system that can be applied to different tasks, rather than building a new model for each task.
There are many theories of cognition. But if you want to work within a framework with the following properties:
Well, then, I'm not aware of any theories which fit the bill as well as ACT-R theory.
You might also be interested in the common model of cognition (initially named standard model of the mind), which is consistent with the ACT-R picture, but also consistent with several competing theories. Think of it as the high-certainty subset of ACT-R.
References for ACT-R
I am no expert on ACT-R, so unfortunatery I can't tell you the best place to get started! However, here are some references.
Books by John R Anderson
John R Anderson is the primary researcher behind ACT-R theory. I have not read all of the following.
John R Anderson also has several other books, which I haven't looked at very much; so maybe a different one is actually a better starting place.
Other References
Here are some other potentially useful starting places.
References for the Common Model of Cognition
If you search "common model of cognition" in Google Scholar, you will find a number of other papers discussing it.
How should we evaluate all this?
I don't personally think about ACT-R very much, but that's because my thinking on AI alignment has little to do with neuroanatomy-inspired AI. Some other people around here think a lot more about those things. ACT-R theory might be useful to those people? Also, if you care about the nitty gritty of human modeling, EG for the sake of inverse reinforcement learning or other value-learning purposes, ACT-R might be useful. It is, after all, a really sophisticated model of a human.
Personally, I am hoping that learning more about ACT-R theory could help me think about human (ir)rationality in more detail.