What's the Point of Continuing the Shutdown?

Over on Facebook, Kathy asks:

Since "flattening the curve" was always about not overwhelming the hospitals and never about preventing the incidence of the disease, then what are we doing now? Put another way, how is opening gradually different than opening suddenly, if the end result is that we'll all eventually end up out in stores and restaurants anyhow while the disease is just as present and threatening? Seems like the only different outcome of a slower opening is further destruction of the economy. What am I missing?

During March, COVID infections were doubling rapidly and at an increasing rate (7 days, 5 days, 3 days), with ~20% needing hospitalization, and killing ~1-2%. That would have overwhelmed ICU/hospital capacity within a few weeks and resulted in ~1,000,000 dead in the US if nothing were done. So we did something: the shutdown. And so far, it's kept infection down within capacity almost everywhere (and spare capacity could be shuffled around).
That plateau also means the R0 number dropped to somewhere between 1.2 and 0.9 in the country as a whole because of the whole social distancing + Stay At Home program. Under local conditions where it's much higher, such as in institutions where distancing isn't possible (prisons, nursing homes, meat packing plants), once the virus gets inside the building, we get a cluster like the 2,000 at the prison in Marion. (This is why large gatherings will be the last to come back.)
Now, we can either loosen up or try for a "suppression strategy". If we had 100% compliance everywhere, infections would have gone to zero in 2-4 weeks, and we would be done. Wuhan managed it in about 35 days from peak, or about 80 days from start of lockdown If we get good (~60-80%) compliance, the R0 goes below 0.9 and the virus can't reproduce fast enough and dies slowly. If you loosen up a little, you may be able to stay under 1.2 and the virus will continue as it is; more than that, and you'll soon lose your grip on it entirely.
In the original models I looked at, that would take the US good compliance and coordination from March through June, at minimum.
If you can't keep everything closed up until the virus dies altogether, you can suppress it until it gets rare enough that you can test everybody and then track contacts. Only infected people would then have to be isolated, and then only until they're no longer infectious. Germany and New Zealand are at or near this stage now.
On the economic side, the thing to realize is that consumer/household consumption drives the economy. Shutting down businesses that would not have consumers, and those whose workers would soon become sick if not at home, is essentially a protective maneuver, putting the businesses in suspended animation rather than allowing them to fail. Paying people not to work under these conditions is a form of social insurance, just like paying people laid off due to flooding or a tornado that destroyed their workplace. It has the additional benefit of keeping money flowing through the economy, so there's demand. Where there's demand, there will eventually be supply to meet it. It doesn't work well the other way around (keeping supply high, but letting demand stay low) because the companies would have no one to sell to.