It's possible mortality rate will be retrospectively revised downward.

You're 92, you're taken to hospital barely breathing, and die soon after. They test the corpse for Corona, and it's positive. You're now recorded as a victim of the pandemic. But in truth was corona really the cause, or was it just one of a multitude of illnesses?

Moreover we simply have no idea how much this is happening.

Somebody could have died this death 3 months ago, and been infected, and nobody would have noticed. Now we look more carefully at the corpses, the death rate from Corona appears to be going up, but maybe it's just we are looking for Corona now, and gradually looking harder and harder?

What we really need to do, is test random samples of the population.