(Not an immunologist/virologist/biologist of any stripe. The following is my rough layman's understanding of the answer to this question. Would love to be corrected by someone with more formal knowledge of the subject.)
My understanding is that the main reason is a biological application of the principle of parsimony: Evolutionarily, organisms don't generally evolve lots of different things all at once. Thus, if you have a novel variant of a virus, it is highly likely to be mostly like existing variants, but with a very small number of changes.
Basically, you can think of it as the virus having to hit a particular threshold of a mutation direction that increases transmissibility to become widely-spread, but also has to hit a particular threshold of a mutation direction that increases lethality in order to become very dangerous.
As soon as it hits that transmissibility threshold, that is the version of the virus that's going to spread, and hitting both those thresholds at the same time is going to be incredibly rare.
What's much more likely (and genuinely concerning) is the possibility that a virus that has already become highly transmissible evolves more in the "lethality" direction and goes from being a widespread nuisance to being a deadly pandemic. The longer we let something like COVID remain widespread, as I understand it, the more likely we are to see a variant emerge that retains its high transmissibility but also gains a higher lethality. However, as we can see from the fact that the bodies are not piling up in the streets, even after nearly a year and a half of a pandemic form of a particular virus, it's by no means guaranteed that something like that will happen, even at a small scale.
My understanding is that the main reason is a biological application of the principle of parsimony: Evolutionarily, organisms don't generally evolve lots of different things all at once. Thus, if you have a novel variant of a virus, it is highly likely to be mostly like existing variants, but with a very small number of changes.
Basically, you can think of it as the virus having to hit a particular threshold of a mutation direction that increases transmissibility to become widely-spread, but also has to hit a particular threshold of a mutation direction that increases lethality in order to become very dangerous.
As soon as it hits that transmissibility threshold, that is the version of the virus that's going to spread, and hitting both those thresholds at the same time is going to be incredibly rare.
What's much more likely (and genuinely concerning) is the possibility that a virus that has already become highly transmissible evolves more in the "lethality" direction and goes from being a widespread nuisance to being a deadly pandemic. The longer we let something like COVID remain widespread, as I understand it, the more likely we are to see a variant emerge that retains its high transmissibility but also gains a higher lethality. However, as we can see from the fact that the bodies are not piling up in the streets, even after nearly a year and a half of a pandemic form of a particular virus, it's by no means guaranteed that something like that will happen, even at a small scale.