If you're not in the Philippines or Vatican, why would anyone seek an annulment instead of a divorce? My understanding is that divorce is cheaper, so even your marriage is invalid, why not just say it's valid and divorce to save money?
I guess we can take cases:
Case 1. The invalidity of your marriage can be proven beyond reasonable doubt.
Case 2. You're not sure the invalidity of your marriage can be proven beyond reasonable doubt.
Also, since this is Legal SE, I guess the answer would be in terms of judicial economy, legislative intent, legal consequences (alimony, custody, etc), state interests, etc.