It would be almost pointless to mandate flu vaccines. The influenza viruses and therefore vaccines change every flu season. They’d have to mandate a new vaccine every flu season. The HPV vaccine is a once and done series of three shots.
Note that cervical cancer deaths in Texas are among the highest in the nation.
Worldwide, influenza kills between 250,000 - 500,000 each year. Worldwide, cervical cancer kills between 250,000 - 300,000. Cervical cancer isn’t trivial.
There is no long term data as to whether or not Gardasil is one series of three shots or if there will need to be boosters. The reason for this is simple, there is no population group of 12 year olds who have even reached the age of 20 yet.
And no they would not have to mandate a new vaccine every year, they would simply have to mandate flu shots every year.