If we're looking at how to do detection right in IT systems, the physical world example you give doesn't really apply all that well. First the environment is different and second threat detection in IT infra is a multi-stage process involving probabilities on each stage. You can't cut the wire and disable them all from one spot. (or you can if you slice the cable, but then you cut your access too - and a bunch of other collateral...)

We deal with imperfect information all the time when building complex software systems.

Let's talk dead node detection, for example, and consensus. "Perfect detection" is impossible due to possible network partition, yet we can build reliable distributed systems on top of that imperfect reality, even in face of malicious nodes (B-F/T). We do this via redundancies; mutli-step 'actualization' of system changes (e.g. transactions); and the ability to revert to a known stable state.

Based on that analog, I think it reasonable to strive for security regime approaches that permit for security failures at component levels. The computational and bandwidth loads may be excessive (ATM) but ultimately there will be systems observing systems and a type of 'security consensus or quorum' theoretical work informing how to build such systems.

There is a thin layer of semantics that overlays the generalized and irreducible state transition due to input: one instance is preventing inconsistent action on data; the other is preventing insecure action on systems.

You can expect single detection system to fail, so you need to make it redundant. For example impossibly loud siren.

Like you said before, any solution is a mix of 2 paradigms.

Another method of defeating a sophisticated burglar alarm system is taking an axe to the power cable to the building.

How many people have a battery hooked up to the siren?

Pretty much every residential system and every commercial system has a battery backup.