I believe filling out the divorce paperwork doesn’t actually make it happen, it’s just an application for divorce.
It has to be filed with the court and a hearing held to make sure it’s all good and then the judge does the thing and you’re divorced.
Mostly this is a rubber-stamping type situation, and the judge mostly makes sure that asset division is done fairly and any children are cared for.
If no one has objections, the money is simple and everyone agrees, and there’s no children the whole thing is relatively simple.

So filling out or destroying the paperwork doesn’t actually do anything.