First: By the time you feel pain, the decay has usually progressed to a more serious level.
If you don't feel pain then your cavity hasn't progressed to a more serious level . That doesn't mean that you don't have to get it pulled . Cavities rarely cause any pain until they have been ignored for a long time and the tooth decay has gotten bigger and bigger. You could use another treatment , tooth extraction isn't necessary but that doesn't mean that you shouldn't. The pain begins when untreated decay reaches the tooth's pulp. When you don't treat the cavity, it will with time create a little hole in a tooth, and if not repaired with a filling, the cavity will simply continue to grow.
Conclusion: If you don't get the cavity pulled off , you will have an abscess or other painful symptoms.
