Fuzzy math. Eliminating 100% of cases in 50% of the communities is the same thing as eliminating 50% of cases in 100% of communities so I'd rather vaccinate 100% of the communities where spread is more likely to occur. Spread is far more likely in New York City than it is in Des Moines, IA.
Take a look at the surge in the Dakotas in the fall. Spread is not just an urban issue.
And don't confusing vaccination with elimination of cases.
You don't need to vaccinate 100% of people to eliminate 100% of cases. First off, even if you vaccinated 100%, you could still get a small number of cases. But you also get diminishing returns with a greater level of vaccination. You can eliminate MORE than 50% of cases, and especially MORE than 50% of deaths, by vaccinating 50% of FEWER of people in a community. Especially if you target the vaccine to those most at risk.
Let's do a rough hypothetic illustration. Two communities of equal population, each averaging 100 deaths per month.
If you vaccinate 50% of the community, targeting those vaccines to those at highest risk... Factoring in that you are getting closer to herd immunity... You can bring those deaths down from 100 per month, down to 20 per month.
So if you vaccinated both communities, at 50%.... You'd get down to a total of 40 deaths per month.
Let's say you vaccinates 100% of 1 community -- bringing it down to 1 death per month. 0% of the second community -- so they still have 100 deaths per month.
In this example, you'd still have 101 total deaths per month.
Point being.... you'll actual eliminate far more cases and deaths by spreading around the vaccine to all communities, than making it all or none.