The lockdown already has saved lives. And will continue to do so, for a while yet. Your simple models don't show it. That doesn't change anything.
The only lives a lockdown saves are ones from an overloaded hospital system. All other deaths are postponed, unless you find a cure or vaccine.
And this is what I mean by simple model. You seem to have decided that infection to herd immunity is the only way forward. That somehow nobody is going to change behavior to reflect a threat, and the only factor worth considering is how long we hit the pause button before adopting the behavior you are familiar/comfortable with.
Maybe you are right.
But I tend to think that when masks are cheap, plentiful, and expected in public, SK style, we can operate in a similar fashion. Masking and contact tracing. Masks suck, but the full range of options suck, and masks seem like the most easily adopted option, as long as this goes on.
It's a virus, not magic. If a significant portion of the population removes itself from the viral feedlot with masking/social distancing/WFH, the situation is much more manageable.
The lockdown functions to remove a significant portion of the population from the viral feedlot until PPE is cheap and plentiful.
This doesn't seem complicated...