You are absolutely right, in an ideal world. But no way do we trust self reporting to be accurate, either. Might capture some cases, but would also have a lot of false negs and possibly false positives. Only one member of a sick family has often been tested even in professional and reporting testing situations. And the mild cases or subclinical cases that go untested? You miss them in those totals anyway. You will always have underreporting.This data doesnt mean much anything anymore and is completely inaccurate due to the widespread usage of at home tests and people no longer reporting positive cases. "Experts" estimate the real world numbers are 7-14x higher than the reported cases now. Personally, in the last 6 months i know at least of about 15 individuals in my immediate family and friends who got it and ZERO of them reported it. The implementation of the at home tests was one of the biggest mistakes of this pandemic. They should have designed it in a way were the output of the test had to be scanned or input into a web site to get the result.
I am happy people have the chance to test at home and self quarantine.
The statisticians do a pretty good job of estimating the total number of cases, and we have solid hospitalization numbers which counts for a lot.
Better to not let perfect be the enemy of good.