CAP therefore shows what real-life trade offs are feasible in the first place ( of course, there are still systems allowed by CAP that might be impossible for other reasons).
CAP therefore shows what real-life trade offs are feasible in the first place ( of course, there are still systems allowed by CAP that might be impossible for other reasons).
CAP is one of the borders of the space. It's popular because it's relatively easy to look at a claim and see if it's on the "possible" or "impossible" side of the border. Tools like that (as in your halting problem example) are extremely useful, because they can be used to cut through a lot of bullshit masquerading as subtlety.
On the other hand, as OP's post does a good job of explaining, CAP is not a good tool for exploring the area inside the boundary. We often use it to do that, and it leads to all sorts of awkwardness and miscommunication. I think OP captured that well, and it's an area I'd really like to see some alternatives getting popularized (harvest and yield, PACELC, etc). Simplified rules are useful in this space, because while it would be very useful for all practitioners to understand the whole taxonomy, there's a lot of material to understand there.
Impossibility results are great, but misinterpreting them and using them to argue stuff to which they simply don't apply is not so great.