I did a little bit of research into cognitive architectures in my undergraduate days, so let me attempt to access the dregs of my memory.
The main limitation you'll run into is kind of summed up from this quote in the wikipedia article:
The architecture often tries to reproduce the behavior of the modelled system (human), in a way that timely behavior (reaction times) of the architecture and modelled cognitive systems can be compared in detail. Other cognitive limitations are often modeled as well, e.g. limited working memory, attention or issues due to cognitive load.
That is the main emphasis of cognitive architectures has been from a psychological angle--modeling human cognition-- not for generic agent building. They're useful, as you state, for performing tasks related to engineering psychology where you want to study the effects of human attention, reaction time, etc on performing specific tasks. Similar to the fighter pilot example you cite. For example, I recall from my brief experience in this area that a lot of attention was paid to simulating minutia such as how well human beings see movement, color, and other features based on the distance from the eye's focus.
So while I think it would be very interesting to try to use a cognitive architecture for an AI, I think its more interesting as an attempt to model a human player then as a competent game AI.
Moreover, as you yourself state, these architectures are just that -- an architecture. They're very generic. Building up to something like a game AI may be just as difficult to do in one of these architectures as it would be in a general-purpose programming language. If you're familiar with the Harvard Architecture of a computer, the following description of the core of a cognitive architecture might sound familiar (from my undergrad paper):
Cognitive architectures divide elements of
human memory between declarative memory, descriptive
memory about things (what a bike is) and procedural
memory, methods for doing things (how to ride a bike).
While the names assigned to units of declarative memory
change per architecture, elements of procedural memory
are almost always referred to as production rules or as
abbreviated productions. Production rules take their name
from their syntax which is of the form: If some declarative
memory precondition is met, then alter declarative
memory. Cognitive architectures execute by repeatedly
selecting production rule(s) whose preconditions are met
then executing the selected rule(s).
So in this very generic architecture, you have to specify all the rules for a game, how to interact with the game, etc in what is effectively a programming language where the code is a set of goals/procedures that are conditionally reevaluated based on memory. This isn't really a very natural way for us to write code :) And if you did want something like this, you could do something similar in a rule-based language such as Prolog. In addition, you'd also need to deal with the human perceptual limitations that the cognitive architecture imposes on the agent (reaction time, visual/auditory limitations, attention limitations, etc) which might not be appropriate in a video game.
In any case, its certainly interesting graduate level stuff in psychology/CS, so if you're doing this just for fun, go for it! It could be a very fun project. But if you're main interest is a good game AI, I'd turn to other tools that can get you where you want to go faster. I'd also go over to the gamedev stackexchange and read their questions on AI.