It's not so much that anyone wants herd immunity.
It's just that the only way to stop outbreaks of this disease is to have enough restistance in the herd to prevent it taking hold. That is herd immunity, and can be achieved either by vaccination (which is months/years away) or by enough people having the disease.
An uncontrolled spike in case numbers would lead to more deaths (NHS overwhelmed) with consequent loss of other health services (greater than amount already taken out, plus many more deaths of HCPs, which has significant impact on ability to rebuild services after - likely to be worse than after a lockdown/controlled peak)
Also if no lockdown/controlled peak, there would be a couple of 'lost months' when nearly everyone had it (wrecking business even more effectively than lockdown), with catastrophic MH consequences from the distress of death on that scale, little means to alleviate suffering of the terminally ill, and bodies unburied because even emergency mortuaries overwhelmed. Plus the immediate lasting social effects of how people would seek to survive when all normalmsupply began to fail.
And of course, the world would not escape the recession/depression would follow the months of devastation.
There isn't a particularly happy ending either way. But flattened peaks is quite possibly the least damaging approach, because then only some economic sectors fail, and the numbers of deaths (including for indirect and post-pandemic deaths) are likely to be less. Not hunky dory, but least worst.