I don't think people are saying to stay shut down until there is a cure. But many are saying we should be easing the re-opening at a slower pace. Looking at all of the case data across the US, most states have flattened the curve, but cases are "steady" as opposed to being on the decline. Many have argued to stay more cautious with the re-opening and do it slower so cases can decrease. I'm not seeing an overall decrease happening yet so the fear is with opening up too early, things will increase again. Time will tell.
It varies based on how one defines "damage".
I don't know of a single scientist who has made the policy. They have given their input on what should be done to the politicians, and the politicians have then made the policy. As for "shaky" evidence, I would rather term it "ever changing evidence". What is being learned about the virus is changing almost daily so recommendations can only be made on best known info at a given point in time.
I liken it to a hurricane. We see one off the coast of Florida and based on its "current" path and intensity, scientists will give recommendations to the politicians of what might happen. Based on a given bit of info, the politicians might give the order to evacuate. Sometimes people evacuate and then the hurricane changes course or intensity and doesn't hit landfall or hits with much less intensity. And some people will follow direction and evacuate, then complain after the fact because they felt they did it for nothing because the storm didn't hit like it was predicted. Or on the flip side some will not evacuate, and the storm does hit (or hits worse than previously predicted) and the results are devastating.
In the end it's a no-win situation, you can only do as best as possible given what's known at a given point in time.