Since you seemed to formulate your thoughts a DP Review a bit more succinctly, maybe we can have a go at answering those questions.
- What does display referred mean
It means you’re editing pixels that have already had a tone mapper applied to them, so how far you can push a slider in a display referred module is limited before artifacts are introduced. Edits are logarithmic (I think, for certain they are non-linear).
- What does scene referred mean
This means edits are done in a linear space. You can push module settings a lot further before the image starts to show processing artifacts.
- What is the practical outcome of using one or tother and which is best for what
The practical outcome is (hoepfully) the same: you end up with an edit you’re happy with. Trust your eyes
The technical difference is that you can push contrast and saturation a lot farther in the scene- part of the editing pipeline than you can in the display- part of the pipeline.
- What is a tone mapper like AGX or Filmic for? Why would I need to use one
To map the linear data from the scene-referred part of the processing pipeline onto the smaller, squished up part of the display. Using a tone mapper gives you easy control for managing the dynamic range of your output medium.
For example, If I edit my image in order to print it on paper, I generally target the Adobe RGB color space and I soft proof my edit on screen with Adobe RGB since my printer supports that color space natively. Now I print my photo and it look like it does on my monitor (give or take reflective vs emissive, etc etc). That is awesome.
But! I just got a new TV that has a much larger color gamut and supports all this fancy HDR stuff (it’s a Samsung Frame TV and its DCI-P3). It has a cool mode call “Art mode” where I can be in a low power state but will show a still image on the screen. A great way to showcase my photograps. But if I just take the Adobe RGB tiff file I exported for printing and put it on the TV, it looks dull and life less and not nearly as good as the print. Because I used my tone mapper, all I have to do is set DCI-P3 as my soft proof profile, and adjust the black/white point in the tone mapper, and now my image is optimized for display on the TV.
- What is the consequence of me turning off all the built in tone mappers, including the old Base Curve and starting with a completely flat, murky image and editing it primarily by dodging and burning with multiple instances of a simple curve tool and masks to restrict it to local edits
It might take you a long time to edit this way. If you have a different display medium (like my TV) that is vastly different than what your original edit was for, then you’ll have to do a lot more wrangling to prepare for that new display medium.
Again, if you’re happy doing what you do, then keep doing it.