All we have done is suppress the rate and yes when we open the case rate will go back up, but we cant stay closed either. Whether we like it or not it has got to run its course like any other disease.
Opening now is a big mistake.
We have eliminated diseases before, and we will eliminate this one too, as long as we stick with what is working. Yellow fever and malaria used to be endemic in the US, but we have so effectively eliminated them that no one alive now remembers when they used to be significant killers.
Right now, the rate of growth of new Covid-19 cases in the US is falling. As long as we keep this up, we will reach a point where there are no more new cases.
The economy will NOT recover if the virus is allowed to spread uncontrollably. In fact, the economic impact will be much worse.