The thing that worries me is the way exponential growth rates work.
In the places that everyone has been paying attention to, New York, Italy, Spain, etc., the growth rate indeed seems to be coming under control. And for the sake of argument, let's say that they/we succeed in reopening businesses while continuing to limit the spread.
But, what about the places that had fewer cases early on, and are now growing at a much higher percentage rate? If you rank countries by the number of new cases, you are starting to see some with relatively few cases but many new ones, and if it is as exponential as it appears, it's going to be a matter of days before the previous leaders are replaced. This is happening country by country, and similarly within the US by state.
The US still had the most new cases of any country yesterday, but who was #2 and #3? Not the countries that you've been hearing about, but Brazil and Russia. Turkey, India, and Mexico also seem to be trending to soon have more new cases than the European countries people have been paying attention to.
And within the US? NY and NJ are still the top two states, but number 3 is now California, number 6 is Texas, and number 8 is Georgia - all states with relatively few cases so far, but the number of new cases is surging relative to the previously hard hit states.
It's like the stock market - people attach too much importance to the numbers describing the current situation and not enough to differences in growth rate.