A loaded question of course, but I'll bite.
1. Nobody is being forced to get vaccinated. It's a requirement for coaches to coach in the NFL, but they can get a different job if they don't want to get the vaccine. Additionally, many coaches, scouts, etc are in higher risk groups (age, obesity, other health issues). For players, it's not a requirement.
2. The vaccine doesn't prevent infection. That's simply not how vaccines work. It provides antibodies that more effectively fight the infection if you get it. This means you're less likely to get sick but if you do, you're less likely to get seriously ill, and have a much lower chance of dying. It also shortens the recovery time, and helps to reduce the spread of the virus. Shorter infection time and lower severity of infection = less contagion spread as there is quite literally less of the virus in the air (at least as far as I understand it).
Getting vaccinated helps to protect you but also your community and especially those who are unable to get vaccinated (young children, people with specific medical conditions).
3. I'm not aware of credible medical sources that suggest getting the vaccine is riskier than not getting it for the average person, regardless of how young or healthy they are.
Of course, if you have some sort of medical condition, like an immune disorder or have had allergic reactions to vaccines in the past, you should talk to your doctor to make sure it is safe for you personally (this is a reasonable thing to do with any vaccine or medication you're considering taking).
So, should we continue to encourage football coaches, players, and the general population to get vaccinated? Yes.