You'd think that would be blindingly obvious, but based on every system in existence ... It's not.
Primarily I think it is marketing/sales since thinking properly about distributed systems is hard and executives don't want to hear about it.
The thing most people pick in practice is CA, single master with hopefully a replicated backup.
That's something lost on a lot of modern engineers, I think. Distributed Systems are something you do because you have to, not because they're the best approach inherently.
The theorem is about being perfectly C, A, and P
If you have more than two hosts, you have P.
If you have delay to sync, you have C.
If you send inaccurate data instead of waiting you have A.
Theres no 'mostly'
so there's a linear relationship between reducing sync time and reducing response time until at some point in reducing sync time you reduce response time below a level you give a shit about...
and you have all 3 of consistency, availability, and partitioning
and then you have beaten the CAP theory
Because you can have a well partitioned system with good data redundancy, and you can take time to let the system become consistent which reduces availability.
But the actual practical outcome of changing availability is changing response time.
Therefore, consistency time is directly and linearly related to response time.
And if the response time is below some threshold that you no longer care about then you have beaten CAP theorem.
So in a practical sense, you can beat the CAP theorem. In an abstract sense you cant.
But response time grounds the theorem to reality because it in every system, there's a point of optimization that no longer matters.