But even a tiny mortality rate is catastrophic when talking about city and country sized populations. The lockdowns happened for a reason, because this disease overwhelms public health.

> most infected have close to no symptoms

Only most of recently infected have no symptoms, whereas most of infected do develop symptoms, but typically after they already transmitted the illness to other people. According to what it is currently known, from all infected around 80% do eventually develop some symptoms, up to 10% need hospital, up to 5% need intensive care and around 1% of all infected eventually die. That is when observed across all age groups, among the older it's much worse.

And as soon as the health system can't cope the percentages of dead increase rapidly to even higher values -- i.e. those that need hospital need it because half of them will need intensive care (and nobody knows before it's critical who), those that need intensive care need it because most of them will need oxygen in some form and half of these will need:

https://en.wikipedia.org/wiki/Tracheal_intubation

That's why it's undesired to have non-functioning health system, and to avoid overwhelming the existing health systems.

That's not accurate. "mild cases" is not the same as "no symptoms".