The time for symptoms to show up is of roughly 2 weeks but the median time is at about 6-8 days. After symptoms show up, it takes a while before people get hospitalized, and then mortality seem to take roughly 21-24 days after hospitalization.

This means that from the time someone is infected until they die, a month and a half can have gone through.

By the time you take new isolation measures, you have to wait roughly two weeks to see if daily infection rates start to vary. But the lethality at this point, assuming no change in healthcare system overload, can be more or less statically predicted for weeks after the fact.

Those are called "lagging indicators"; the main thing you try to prevent are deaths, which you can lower by reducing the overload on the healthcare systems, which you can lower by controlling infection rates and keeping them low.

Due to the duration of the disease's evolution, you get to see if your policies really worked more than a month and a half after enacting them, which is extremely slow for a disease that propagates at exponential rates. So people look for proxies like infection rates that are still lagging, but far less so.

Do note that the one good metric you want in the end is going to be "excess deaths", which counts the impact of not just the diseases, but of all other side issues that the disease may have caused. This can usually take months up to years to properly account and analyze.