This of course assumes certain levels of mitigation strategies, without those, the HIT would shoot up
Isn't herd immunity supposed to stop further infection without other precautions? IMO, if still social distancing, masks and more importantly curbing of any economic activities are required to stop spreading infection, then its not herd immunity.
Saar, I think you might be making the mistake of regarding this "herd immunity" as a fixed number. As a rough analogy (don't try to match all points, it's just an analogy):
If you jump off a plane, you will gain speed, until the "terminal velocity." This is the speed at which the air around you resists your fall to the same extent as your weight, so you stop gaining speed. For a human in the earth's atmosphere, this terminal velocity is around 40 to 50 m/s (50 m/s = 180 kmph ~= 110 mph). It's more than enough to splatter a human to pulp, even landing on water. But anything smaller than a field mouse can fall from any height on earth, and safely hit the ground and scramble away, because it's terminal velocity is much smaller. On the moon of course, no atmosphere, so the same animal (smaller than a field mouse) will still get pulped if it drops from a sufficient height.
But this "terminal velocity" for a human is not a hard value, if a human spreads hands and feet apart and maximizes surface area when falling, the terminal velocity will reduce (not enough to prevent pulping, though), whereas if the human adopts a "dive" position or curls up into a ball, the terminal velocity will increase. If the human carries an open umbrella (which doesn't get ripped apart) the terminal velocity will reduce further, but a parachute will reduce the terminal velocity to a few meters per second, allowing safe landing.
Now if the human wears a parachute, attains the terminal velocity of a few meters per second, and then thinks - "ok, I've got to terminal velocity, I don't need this parachute anymore" and rips it off, then the human will accelerate to the new terminal velocity (glide/ fall - 40 to 50 m/s). His/ her fall will still stop accelerating at the terminal velocity, only that value is now much higher. Of course, once the human lands safely, then the parachute can be ripped off, there's no more need for it at that point.
For the epidemic - with mitigation efforts (parachute), the HIT (analogous to terminal velocity above) could be 20%. Without those mitigation efforts (free fall), it could hit 60%. If the population adopts mitigation efforts and brings the epidemic to a stop (no more spread) at 20%, and then thinks "why do we need these mitigation efforts anymore?" (ripping off the parachute too soon) then the HIT will rise to the new value of 60%, and the epidemic will continue until it hits that value (the human will accelerate until the higher terminal velocity). So the need is to keep the mitigation efforts/ parachute going until "safely landing," which is the point where there are *no more active infections.* At that point, all mitigation efforts can be stopped (the parachute can be ripped off) and there is no more risk.
With vaccination, the strategy is to get beyond the value of the *unmitigated* HIT, so that people can continue with their normal lives. It is also possible to vaccinate for a *mitigated* HIT and then have people wear masks/ social distance etc., but they will have to do all that until there is no more risk, else the natural infection will continue (beyond the point of vaccination) until it gets to the *unmitigated* HIT.
So you could vaccinate 90% of the population and have them live normal lives. Or you could vaccinate 40%, and have them social distance and wear masks, that will also work (with the attendant inconvenience). They are both representative of "Herd Immunity," only, in one case, it is an "unmitigated" HIT, in the other, it is a HIT which needs further mitigation. By adjusting the level of mitigation, the HIT will vary over an entire spectrum from 0% (complete distancing - one guy per city level) to close to 100% (Alabama nutters).
Hope that makes sense.
EDIT: Further word on 'dem Alabama nutters. The media has fed them a steady stream of messages to the effect that "The Terminal Velocity is 50 m/s" so they work on that assumption that "let's get to that velocity as fast as possible, and then we're fine." So before jumping off that plane, they each grab a big 'ol block of lead, so they can accelerate to that terminal velocity as soon as possible. But by doing that, they've greatly increased their terminal velocity to say 100 m/s. Also there might have been some chance of surviving that 50 m/s fall (if *very* lucky, there have been instances of people landing on snow and surviving), but at 100 m/s, straddling a block of lead?? Not a chance.
So the media tells them that "The HIT is 60%" and they try to race for that by having COVID parties, that alone increases the HIT, not only that, the death rate also shoots up because of higher viral loads and greater risk taking in general. But the media doesn't bother telling them that, because the media itself hasn't bothered to educate itself - "60% HIT" is not written in stone, it can vary from much less than that to much more than that, depending on the behavior of the population.