The optional add-on feature for events is complete! See Event Items and Sign-up Sheet improvements. 
@hheiber You can always trigger an event invite email whenever you like by editing the event and setting the invitations to be sent “Today”. Automatic invites are available 1-7, 14, 30, 60, 90, or 180 days before the event, but options will be hidden if the event is too soon for them to be applicable (so an event 10 days away will only show the options to send invites 1-7 days before).
Also, sending event invites to only people who haven’t responded isn’t a feature (yet, it’s a good idea), but event invites don’t get sent out to people who’ve RSVP’d “No,” so you won’t accidentally spam them.