Aren’t all these mutations going to make it unstable?
Stability has a specific meaning in the world of virus replication. A stable replication is one that is precise. Precise means in this instance that the newly-created virions are exactly the same as the virus that infected the production cell.
Coronavirus in general are unstable. That’s why they are mutating so quickly. So your question is excellent because the relationship is mentioned but it is reversed. The virus being unstable is what generates mutations, not the other way around.
In terms of what you want, if a current type of virus is very dangerous, you want stable vs unstable based on if you think you can make a vax. If you can, you want a stable virus like smallpox that doesn’t mutate away from the vax. If you can’t make a vax you would probably want an unstable virus, so it can mutate to something you maybe can deal with.