That's just flat out wrong. If that were the case, than the Spanish Flu would still be killing millions of people per year.

SARS-CoV-2 and A/H1N1 aren't even in the same phylum. It would be silly to expect them to have precisely the same effect. Besides, when people gush about "herd immunity" they don't usually include the caveat "of course it's going to kill fifty million people first!"

There have been what, three cases of people being infected twice? And they barely got sick?

The antibodies from infected people are being shown to last somewhere on an average of 3 months.

Kinda hard to be immune if you have nothing to protect you.

How sick you get from the disease is irrelevant in this context.

Your understanding of the immune system is not quite correct. Just because you can't detect antibodies doesn't mean you lack immunity.

B-cells can stop producing antibodies and reactivate production in response to an antigen. T-cell memory appears to be quite robust for coronaviruses (and this one in particular)

To establish a lack of durable antibody response, challenge trials would need to be done, where the host is challenged by the virus (or something that looks like the virus like it's spike protein). These trials have not been run.

We can only guess without data specific to SARS-COV-2, but for seasonal coronaviruses, antibodies disappear after ~6 months and reinfection with the same strain can occur after 1 year.

It isn't entirely irrelevant. If you can get reinfected but not get sick twice, it's as if we reached herd immunity at 100%.

And it's perfectly normal that antibodies don't stay in the bloodstream forever. The immune system remembers how to make them and can produce new ones when needed.

Reinfection is problematic for herd immunity strategy as it keeps the transmission rate , R high. This keeps the less healthy vulnerable.