I would look into China's experience for guidance. I know the costs would be monumental, so it's not an easy decision, and would not like to be in her shoes right now. But if the alternative is what Merkel suggests...
But this virus won't go away until a significant fraction of the population gets infected and heals. It'll come back in the fall when it's colder and hit again. I'm afraid the only principled solution here is to develop vaccines and working antivirals in the next few months, which by "normal" standards is completely unprecedented.