An option to prevent the submissions of a form from being stored on the site would be nice to have for privacy sensitive forms. Could be a global and per form setting.
I’m not sure I know what you mean here. Where would you store it instead of the database? The “Form Submission” post type is already hidden from the public and only appears in the WordPress dashboard.
You would need to have at least one form action configured that sends the form data somewhere else, and this proposed option would prevent the submission from being stored in the database and thus not appear in the Form Submissions post type. It’s a privacy option and useful for cases where you’re collecting data you’d rather not store on the site.
For reference, Forminator Pro has this option: https://wpmudev.com/docs/wpmu-dev-plugins/forminator/#data-storage