Although I rarely use the Split Tone panel in the Develop module (and I bet you can say the same), there are a couple of situations in which I find it extremely useful: Toned Black and Whites and full color nature scenes that are designed for emotional impact.
Here’s a black and white in which I first used the HSL panel in Grayscale mode to adjust each of the primary and secondary colors to give a black and white exactly the tone shades in black and white that I want. Then I used the Split Tone panel to assign blues to the Highlights and Sepia to the shadows. You can see the color, black and white, and split-toned versions in the illustration below.
Here’s a Sunset in Guayabo, Costa Rica, first as it looked when I adjusted the color as I normally would, then when I used Split toning to emphasize the reds in the Sunset sky and the greens in the tropical lushness of this pasture.