Although this would be a good outcome, my understanding is that the inherent mutation rate of the virus makes settling on a single variant or family of non-dead

Although this would be a good outcome, my understanding is that the inherent mutation rate of the virus makes settling on a single variant or family of non-deadly variants unlikely. Even if a variant became endemic with a death rate of 0.05% for example, unless this mutation is at a near global optima in terms of transmissibility, I imagine it would be a precarious situation.