Hi there,
While there is no setting or toggle you can use to disable storing the form submissions in your database, you can use a filter to customize the behaviour of the form feature to fit your needs. The grunion_contact_form_success_message
filter, for example, could be used to delete form submissions immediately after the email has been sent. You can check this page of the Jetpack codex to find out more: https://developer.jetpack.com/hooks/grunion_contact_form_success_message
You’ll be able to paste the second snippet on that page in a functionality plugin and that should help.
I can understand you may not find this feature useful, others do rely on the messages appearing in their dashboard, and use the Feedback menu as part of their workflow. It’s especially useful for folks who do not rely on email much, or who use another plugin to automatically process those form submissions for another purpose (like newsletter management), or folks who work as part of a team when not everyone on the team has access to the mailbox where the emails are received.
In any case, I do see your point that in some cases it is not needed. This is not a request that’s come up a lot in the past few years though. In fact, more folks have suggested that we should not send any email and instead only store the forms on the site. To answer that need, we added the grunion_should_send_email
hook: https://developer.jetpack.com/hooks/grunion_should_send_email
If, however, we receive more feedback about this in the future, we’ll definitely consider adding an option to the Jetpack form settings, so one can disable saving forms to the database as they set up a new form. Until then, the workaround I mentioned above should work.