But why are we only considering vaccination with regards to herd immunity. Shouldn't we also be including natural immunity from previous covid infection?
Because, for example in Canada, there have been 1.4 million total cases of Covid over the last year which has on multiple occasions stretched particularly ICU capacity to the limit. In a much shorter time period we have administered 27.7 million doses of vaccines. We give more doses every 3 days than we had cases in 14 months. Natural immunity is almost negligible compared to vaccination. Getting to herd immunity levels with actual infection will result in hundreds of thousands of deaths and damage our health (and healthcare system) for decades.
It has been demonstrated that repeated infections are possible and may be common. And there are a large number of variants in the wild that are not hindered by immune systems previously exposed to other variants. Allowing the virus to spread in populations causes even more variants to emerge.
Even vaccines provide reduced protection from new variants. I read today that most effective vaccine only provides a ~70% chance or so of protection from the Delta variant in the UK. Hence the talk of booster shots before the initial vaccines were rolled out.
Herd immunity comes from vaccination. It's not really feasible for it to occur naturally because the virus will continue to mutate and reinfect people indefinitely.