My understanding is that it is necessary to slow the progression to “flatten the curve” below hospital capacity, and that extra time for building increased hospital capacity is a nice side effect but not the primary goal. Basically, when more people get sick than the hospitals can take in, the mortality rate skyrockets, which is why Italy has more reported deaths than China right now.
Edit: Here’s the old paper from 2007 the CDC is using to inform some of the policy around “flattening the curve” below hospital capacity.
https://stacks.cdc.gov/view/cdc/11425
But after the three month delay, you’ll have the same exponential growth, if life goes back to usual. It’s even present in these plots, at the right hand side (see California). It’s unfortunate the plots aren’t extended more to show longer term trends.
Edit: Here’s the old paper from 2007 the CDC is using to inform some of the policy around “flattening the curve” below hospital capacity. https://stacks.cdc.gov/view/cdc/11425