What is your back of the envelope math here? Clearly, the vaccine does not prevent infection. There is no evidence it reduces the incidence of harmful sequelae following infection. So how does this add up to support mandatory vaccination for young men?

There are tons of papers showing the exact opposite of what you said if actually cared to look.

Going to be a little hard to credibly show the vaccine protects against infection when everyone is getting infected.

Knowing whether someone is vaccinated against COVID is not going to help you predict whether they have been or will be infected. Knowing whether someone had the smallpox vaccine is going to help you predict whether they had been or would become infected. See the difference?