As far as my understanding goes, herd immunity is not a real alternative to vaccinations. Herd immunity means that a very large percentage of the population, spread evenly across every community, would have to be infected and recover, another commenter cited a source estimating between 50% and 80%[0].
This means getting basically everybody infected, the reason a vaccine would be necessary is that we don't want everybody to get infected because it carries significant risks to health and life with it.
Also the timeframe needed to reach such high percentages of immunity would be very long. Looking at the US, if you assume a continued infection rate of 50 000 new infections each day (much more would probably mean overwhelming hospital capacities) it would take 8 years just to reach the 50% threshold, 13 years to reach 80%. Lot of time and suffering saved by going the vaccine route.