If the purpose of the analysis is to determine whether the preventive measure is effective and not overwrought, an excess deaths analysis is a good one because it helps infer what the toll would be in absence of the measure.

How do you know what the toll would be in the absence of the measure? Excess deaths tells us how many deaths are from virus+shutdown. I don't see how we can use this data to find out how many deaths there would be in a virus (no shutdown) scenario, or in a shutdown (no virus) scenario.