Spoilers: Daily Integrity Checks are not only a best practice, but they also provide a snapshot of global sizes and density. 
Update 2024-04-16:  As of IRIS 2024.1, Many of the below utilities now offer a mode to estimate the size with <2% error on average with orders of magnitude improvements in performance and IO requirements. I continue to urge regular Integrity Checks, however there are situations where more urgent answers are needed.