It’s an interesting counterfactual. I think most on here can also agree more people would’ve died, faster.
For my money the right approach was tying it to hospital availability. If we were going to overwhelm that then we had a problem and had to stay at some level of shut down.
Of course, knowing what we know now, had we “burned through” a lot of cases quickly, before the much less severe delta strain developed, we would’ve been trading a lot of mildly sick people for a lot of really sick people.