The models predict Sweden will overwhelm their hospital capacity in about a month.
I think the Swedes are distancing more than the model is allowing.
Getting back to the logic for a government "stay at home" order, I think it makes sense to look at national trends...
In Sweden, people have trust in their government. The Swedish government basically said "work from home if you can, vulnerable populations should stay secluded, no large gatherings are allowed, try to social distance from each other, be safe, and take this seriously, but we're not going to mandate business closures or stay-at-home orders."
To a large extent, Swedes followed the guideline. They voluntarily took many of the actions that the government might have mandated because their government said they should.
That's, uh... Not exactly how it would occur in America. We actively distrust our government. Sometimes Americans need a sort of whack upside the head. If the government had just "suggested" we social distance, do you really think anyone here would have taken it seriously? I personally don't. Right now the government IS mandating it and a lot of people aren't taking it seriously.
I think the government mandates were a sort of whack upside the head to give us all a mental "reset" that this isn't a joke. Which--if Sweden's experience remains good--gives us a blueprint for starting to reopen the economy.
If the messaging is right, i.e. "we're going to slowly and carefully re-open, but you all still need to be vigilant or this will get out of control", I think people will follow that messaging much more readily than if America has followed Sweden's messaging from the start.