China has admitted their ‘death’ numbers are only those who die from covid pneumonia. They’re not counting sepsis, heart or renal failures.
Herd immunity works good against a stable virus or bacteria. One that’s constantly mutating, not so good, if achievable at all. Consider the flu - around every year for centuries, yet lots of people catch it every year because the flu strains keep changing
I doubt that Covid will be as variable as the flu.
The introduction of new flu viruses from animal reservoirs such as swine and birds happens quite frequently.
New coronaviruses from bats and other hosts seem less frequent.