That's happening right now with Sweden and it's sure to be a pretty interesting case study. Their health system hasn't yet been overwhelmed, but they've had a lot of cases (and a lot of deaths), especially on a per capita basis for a smaller country:

https://www.theguardian.com/world/2020/apr/15/sweden-coronav...

Of course, some right-wing media outlets have still been touting this as a success and a model for a less economically-damaging approach— this article is from nine days ago, but it's not hard to find other similar ones:

https://www.nationalreview.com/2020/04/coronavirus-response-...

It's probably much too early to say one way or another, but I guess there is some value in having multiple approaches be tried. Particularly in a world where guys like Glenn Beck have gone on record saying they'd "rather die than kill the country."