So, it wouldn't make for an exciting movie or any sequels, but why doesn't anyone try to destroy Annabelle, like set her on fire or throw her in a wood chipper?
A conversation between Ed Warren and a reporter visiting his house from the beginning of The Conjuring
Reporter : Oh, ahem. Well, isn't it scary, or doesn't it worry you...to have all these items right in your home?
ED: That's why we have a priest that comes by once a month to bless the room. Well, the way I see it is: It's safer for these things to be in here than out there. It's kind of like keeping guns off the street.
Reporter: Why not just throw them in an incinerator? Destroy them.
Ed: Well, that would only destroy the vessel. Sometimes it's better to keep the genie in the bottle.
Reporter: Say, is the, uh, Annabelle doll here?
Ed: Right this way....
I'm not sure this fits proper stack exchange criteria, but essentially this comes down to a disconnect between what's true and what the movie exaggerated.
What's True - A Raggedy Anne doll was said to be haunted and it wound up in a glass case, not in the home, but in an Ed and Lorraine Warren's occult museum, presumably, at that point, the Doll was no longer a threat or it would have been quite irresponsible of the Warrens to put it in a museum and let people see it. In real life, they made money using the Doll as something for people to come to see. Source.
So, based on the fact that the doll was never destroyed in real life, but instead, kept behind a glass case, that's what they did in the movies.
There is some inconsistency, as destroying or exorcising possessed objects makes sense if you accept the premise of the films. What's loosely implied in the movies is that they keep the doll in a safe room of sorts in their house that only they enter, not their children. Presumably Annabelle was too strong to be "de-possessed". That seems to be the argument the movie is making.
If you read about possession and the like and you believe in such things, which I used to a little bit, not much anymore. Burning a possessed object can be very dangerous. Burying is recommended, not burning. (Source, Ouija the most dangerous game - a book I read about 20 years ago). - too hard to pull the quote.