'Exercise' might marginally improve your chances of defeating COVID, but in order for it to have a material effect for most Americans it would take literally years of complete transformation of habits.
Furthermore, even that would not be remotely as beneficial as vaccines or social distancing, maybe not even masks.
Vaccines >>> Doing Cardio.
The reason the government probably does not talk heavily about 'eating well' as some type of 'response behaviour' to COVID, is because people will get the 'Joe Rogan' mentality, and believe that 'Good Nutrition, Hitting the Gym Hard, and Positive Mindset' will just 'Alpha' their way past COVID, when that's definitely not the case, i.e. people would get a vastly over inflated sense of what their likely trivial lifestyle changes will do.
And of course:
"yet they insist that relatively new novel vaccines have absolutely none" (side effects) - which is blatantly and offensively false. Literally every article about vaccines talks about their numerous direct side-effects that almost 80% of people exhibit. And literally 100% of vaccine recipients are warned directly of these, including symptoms of myocarditis, signs to look for and when to call a doctor.