There are already several issues for improving the "Fields" tab (which has really horrible UX, of course), but I think there is now a consensus, more or less, to imitate Views' solution for this – only list the indexed fields and provide an "Add fields" button to add more. In a first step, this wouldn't even have to use a modal dialog, it could just be a normal form on a separate page, too. Changing it to a modal would just be polishing.
(I also don't know whether separate forms for our few settings for each field would make sense – probably not until we add more introspection to "Add fields" processors, and then this might still be incorporated into a single form much better.)
One thing that would be needed here, though, which probably isn't trivial, is a good way to add related fields. Probably some AJAX magic to load the related fields, up to arbitrary depths, on demand, also making the "additional fields" configuration for indexes unnecessary.
Estimated Value and Story Points
This issue was identified as a Beta Blocker for Drupal 8. We sat down and figured out the value proposition and amount of work (story points) for this issue.
Value and Story points are in the scale of fibonacci. Our minimum is 1, our maximum is 21. The higher, the more value or work a certain issue has.
Value : 13
Story Points: 21