The initial hope seemed to be that if enough people were infected and recovered, the potential of immunity (and subsequent herd immunity) could allow some earlier gradual return to activity. Preliminary information seems to be coming in on that.
I'm not an expert in this area at all, but from reading it seems a threshold for herd immunity required for something like the flu is 30-40%. Not sure how much transmissibility dictates this threshold https://www.technologyreview.com/2020/04/09/999015/blood-tests-show-15-of-people-are-now-immune-to-covid-19-in-one-town-in-germany/
A worrying development however is the report from South Korea about 'reactivation' of the virus in recovered patients. This could be from an unlikely case of failed consecutive tests (or the diagnostics are not reliable enough) though. https://www.bloomberg.com/news/articles/2020-04-09/coronavirus-may-reactivate-in-cured-patients-korean-cdc-says
In any case, many of the countries that seemed to have had a better response to the outbreak are now seeing new spikes in cases. https://twitter.com/nytimes/status/1248526139825537025?s=19
So it seems so far the more likely approach until a viable vaccine is available is the scenario laid out in the Imperial College report (not sure if the timelines still hold since real world data seem to be coming under the forecasted figures and NHS capacity has also increased)
An expert's look on the pieces mentioned in this thread https://twitter.com/mlipsitch/status/1249646012341329920?s=19