You really want to find every single person who has been infected with the mutant strain and find out how sick they got. If you find a mutant that infected 10,000 people and didn’t cause any serious illness then you have a pretty good idea it safe.
If it is a rare strain, how will you know if it's safe? Seems like it would have to be a rare strain with thousands of cases and hospitalizations in that population are extremely rare.
Sampling bias and other confounding factors would be a real problem in this search, at least from a statistical point of view, imo.
I also think finding everyone who has been infected with a strain isn't feasible, at best you are sampling from the population.