Why not have old and unhealthy people quarantine themselves at home for a month, and have everyone else intentionally infected with coronavirus to build up herd immunity?

There’d be minimal economic disruption since most would be so mildly sick they could keep going to work, and most work is done by young healthy people anyway.

Moreover, with a vaccine years off and this thing spreading out of control everywhere, what alternative is there? (Besides total societal paralysis for months and months to come).