It is unlikely but possible that suicides from the shutdown will exceed deaths from the disease. But it is absolutely not true that they will exceed projected deaths from letting the disease run its course unchecked.

Here is a parallel. We are afraid of buildings catching fire, so we build sprinkler systems into them. But the result is that in actual fires, the water damage from the sprinkler system exceeds the damage from the fire. That's because there is a fairly small fire and a big wet area from the sprinklers.

Is this an argument for not having the sprinkler system? Of course not! Because the damage from the sprinkler system is far less than what the damage from an unchecked fire would have been.

By my estimate, the deaths in the USA alone, with no lockdowns, is around 2 million this year. Other attempts that I’ve seen to estimate it come out with similar figures.

A too-large rush of cases will overload our system and result in medical providers succumbing to the virus as well, resulting in it shutting down.

That would result in millions more suffering and possibly dying.

That might make you think a ventilator surge might save 10-20% of people who otherwise would have died. But that's not true because we can choose who gets the ventilators. The actual difference in death rate will be small because we will stop ventilating the cases that still have a 95%+ chance of dying even with ventilating. Ultimately, the impact of the ventilator surge is going to be a bunch of 80+ year old patients with significant comorbidities getting pointless interventions. It's going to save few lives and will only marginally impact the mortality rate.

Every day of delay increases the chances of treatments being more available and better understood.