A huge problem I see with this is that already circulating coronaviruses cause immunities as short as 3 months. While the SARS virus seems to cause much longer immunity (same for MERS), this may be linked to the strong symptomes that people have, thus may be due to a stronger immune reaction. Asymptomatic cases and people with mild symptoms may therefore be immune only for a short time. If this is the case, any herd immunity strategy will achieve not much but endanger many many people.