I wonder if the old cases were essentially hidden in the larger number of cases caused by smoking? With smoking on the way down, the percent of cases that would be attributable to HPV would go up. Trying to find the throat cancer rate by year for the past few decades and not having any immediate luck though.

Edit: This data from the CDC seems to indicate that the increase is in number of new cases, but the rate has been fairly flat since 1999 https://gis.cdc.gov/Cancer/USCS/#/Trends/