I'll be less familiar with the details for the US and the reporting in individual states, but I can comment on what we've been seeing in the UK.
When the pandemic first hit, we had very little testing and people were also told to
NOT visit their GPs (doctors) in order to reduce the spread and they were not tested. The main concern was to limit the spread and we were still gearing up for the pandemic, we simply did not have the testing capacity in place yet. In other words, our number of cases during the first wave were likely to be very significantly underestimated. The testing improved over the coming months and people were then encouraged to get one of a variety of tests if they showed any symptoms, and so we have a more accurate (although not perfect) picture of the situation. Testing has come along further still now, and parents with children at school now have twice weekly lateral flow tests (although imperfect) and then go for a different test if one of these gives a positive result.
Bear in mind that it may take something like roughly 4-14 days for people to develop symptoms and get tested, and then it is typically a few weeks between infections and deaths. So there will always be lag in the graphs we see, whether we compare cases and hospitalizations, cases and deaths, lockdowns and cases, re-opening and cases, etc. Always take this lag into account when looking at data.
I've noticed an earlier link I provided now does not work. So, I've grabbed some data from Our World in Data (
https://ourworldindata.org/covid-cases) and annotated one of the graphs. The government here has made rather a mess of things with complex (and inconsistent) rules, opening up, locking down again, and so on, so I've included some of the key points only... Hopefully the data is helpful.
To me, it is clear that lockdowns do reduce the number of cases (and therefore deaths). They may be brute force for protecting the population and the healthcare infrastructure, but they work. The other options are vaccination and/or very carefully managed testing and tracing. New Zealand and a number of Asian countries have done well.
With any lockdown, it is also important that: the restrictions are strong enough, the rules are clear, and that the public follow them.