I think the history of this is something like:

- it was an expensive vaccine

- it was therefore initially introduced to women as a cervical cancer thing

- HPV however hits men at around half the cancer rate of women but through throat cancer

Or something like that. So actually the benefit to men is of a similar order of magnitude as that to women but it was just given to women to save money. Every child should be given it.

Edit: Total Rate (of HPV caused cancers) in Women: Approximately 15.9 cases per 100,000 females per year.

Total Rate in Men: Approximately 9.3 cases per 100,000 males per year.

Edit 2: Severity-Adjusted HPV Cancer Burden:

When adjusted for the severity and impact on life, the relative burden of HPV-related cancers shifts. Cancers with higher mortality rates and more debilitating treatments, like oropharyngeal cancer, carry a heavier weight.

Total Burden in Men: Approximately 135 DALYs per 100,000 males per year.

Total Burden in Women: Approximately 125 DALYs per 100,000 females per year.

The HPV vaccine became part of the government vaccination program for boys/men 6 years ago (almost to the date) precisely for the reasons you mention. Personally really happy to see this as there was some initial fear mongering related to the HPV vaccine some years ago.