What things cannot be tested(except by elimination) when trying to diagnose a sluggish engine?

I would start by looking at what a car engine needs:

• Air intake. You specified most of the intake sensors, but not the air filter. Remember to check the air filter! In turbo/supercharged cars, the turbo/supercharger needs to work, obviously. Some newer cars have a drive-by-wire system to control the throttle electronically, but I assume it would show on the warning light if it's faulty.
• Compression. You said it's fine. Easy to test, so I presume it is fine.
• Ignition for spark-ignited engines. You said it's fine as well. However, there may be problems in wet weather that won't occur in dry weather, so if you have weather wetness dependent problem, it could be the ignition.
• Exhaust. If something (such as clogged diesel particulate filter) is blocking the exhaust flow, that could be a problem.
• Fuel injection. You completely neglected the fuel system, such as fuel pump, fuel filter, fuel injectors etc.

I would say that's about it. Some engines have variable valve timing (VVT), so if the VVT system is faulty, the messed-up valve timings could affect performance.

Did I already mention warning lights? Even a pre-2000 car could have a warning light on, so a code reader will tell what it's about. I used to have a 1989 Opel Vectra that could morse the code using the warning light when two pins on the ALDL connector were connected together, so a code reader isn't always necessary.

Edit: when re-reading the question, it seems to be about only those problems that can be tested only by elimination. My answer is more general. I won't delete my answer, just leaving this additional edit here to warn readers.

Even on my 94 Integra, as long as I have a scanner I can connect, I can watch a live input of the sensor and output of the ECU.

Anything can be tested. It is just a matter of time (to take things apart and test), and money (to test replacing suspect parts).