Once the growth is no longer exponential, measures can be rolled back slowly, especially if they have access to enough tests, masks and respirators.
The earlier action is taken, the cheaper it will be to stop this. Every week of delay can increase casualty rates by a factor of 10. A month of delay, can mean the difference between 10000 and 10 million dead.
Also, economic costs, both in direct treatment cost as well as the disruption to the productive side of the economy will rise sharply the longer we wait. (Well, at least if we don't see the death of sick and elderly as an economic benefit.)
People will continue to get the Flu, Colds, HIV / AIDs even throughout this whole shebang. We need to know COVID19 cases specifically, to know if our lockdown methodology is being effective.