You're assuming that once someone is vaccinated they have immunity to that particular pathogen,
Where exactly do I say that?
but that immunity decreases with time.
Really?
For example all those vaccinated with Varicella in the last 10 years, how many are still immune?
Probably a lot more than you think.
"In Japanese studies, 97% of children had antibody 7 to 10 years after vaccination."
"Immunity appears to be long-lasting, and is probably permanent in the majority of vaccinees."
https://www.cdc.gov/vaccines/pubs/pinkbook/downloads/varicella.pdf