Most folks have a case of covid, and are then done with it. There's "long-covid". But there's also the problem of those with weakened immune systems that never quite clear the infection, and it is in these individuals that variants are most likely to arise. They are also typically among the folks who can't get vaccinated.
So, we really need to vaccinate everyone we can, to protect those who cannot, because those who cannot are the ones most likely to generate a variant that might evade the vaccine.