To be clear, there is no solution to this problem. No amount of software configuration will fix it. Dell engineers have confirmed that this behavior is controlled by the display firmware.

Last I heard, Dell is working on exposing a switch in the BIOS that would disable the adaptive contrast feature, although they would not give an ETA on when that BIOS update would be available. (source)

There is an optional firmware update available for the QHD+ model that allows you to disable the adaptive contrast feature. You will have to contact ProSupport to get it.

For the FHD model, it is not possible to disable it since the display firmware for the FHD panel is not updateable. Dell will not repair it or replace it since the engineering team says that it is functioning as designed and therefore, not a "problem".

Source: https://github.com/advancingu/XPS13Linux/issues/2#issuecomment-151708470

(Jared Dominguez is a Dell employee who works on their Linux team for consumer products [Project Sputnik.])

Edit: Note that the above applies only to the XPS 13 (9343), i.e. the model with a 5th-gen Broadwell processor.

For the new XPS 13 with 6th-gen Skylake processors, the adaptive contrast feature is disabled by default on the QHD+ model only. The FHD model of the Skylake XPS 13 still has it enabled, and the situation for that model is identical to the Broadwell FHD model.

Edit 2: Whoops, I should've read more carefully. This situation applies to both the XPS 13 (9343) with 5th-gen Broadwell processors and the new XPS 13 (9350) with 6th-gen Skylake processors. 

However, it is disabled on the new XPS 15 (9550) with 6th-gen Skylake processors.

Employees within Dell had requested that it be disabled on the new XPS 13 too, but that model was too far into development/production to be changed.