Failure in this reasoning is that if these people in nursing homes get covid, they are still sent to a hospital and they will occupy an ICU bed - denying it to them just because they already "lived their lives" would be an abject failure of a human civilisation and unacceptable to any normal person.
And thus, they will add to the lack of capacity of hospitals and reduce the success rate of treatment of other patients, Covid and not.
There are few people in nursing homes, vaccine can get to them very quickly, it will not delay vaccination of other groups including frontline workers by so much, but it will approach epidemic from the opposite side: 1% of people - the most elderly, sick and frail - have 50% of covid deaths among them so by vaccinating 1% of people we are cutting these in half, which at the current R number of about 1.1, saves 7 weeks of time, while requiring at most 2 weeks of time. Lives are saved by doing so.
