umm.edu/health/medical/reports/articles/shingles-and-chickenpox-varicellazoster-virus
Since a varicella vaccine became available in the U.S. in 1995, the incidence of disease and hospitalizations due to chickenpox has declined by nearly 90%.
There are two types of varicella vaccines:
A chickenpox vaccine for vaccinating children, adolescents, and adults
A shingles vaccine for vaccinating adults age 50 years and older
And immunisation increases the risk of shingles so is not necessarily a suitable public health intervention.
That statement is a little miss leading:
www.ncbi.nlm.nih.gov/pmc/articles/PMC2563790/
Vaccine strains are, as far as we know, less likely to reactivate to cause shingles.
It is not necessary to vaccinate everyone to reduce chickenpox to very low levels—to cause an infection to die out in a community it is only necessary to vaccinate a sufficient proportion such that the average case on average transmits the infection to less than one person.
However if your talking not about the vaccinated DC but the older population:
Mathematical models predict that shingles in the unvaccinated would initially increase by 30%–50% if childhood vaccination rates were high, and would decrease thereafter. Combined results from three studies suggest the increased incidence of shingles would last for 30–50 years and would affect mostly those aged 10–44 years at the time of vaccine introduction.8,11,12 The greater the chickenpox vaccination rates the higher the initial incidence of shingles would be until everyone was vaccinated (in other words until those of us my age who harbour varicella zoster virus in our nervous ganglia die off).
It's possible to vaccinate both elderly with shingles vaccine and young with chickenpox and avoid that issue so it not being in the public health interest isn't clear cut.