What, exactly, is angle of repose, and where is it in this image?
Geological materials such as sediments are never totally homogeneous. There will always be softer and harder regions within sedimentary deposits.

The fact that erosion channels have been created is due to the force/energy of the water creating the channels, the extent of the force the water had when it created the channels, the softness of the material being gouged out and the hardness and cohesion of the material left behind.

The angle of the walls of the channels is not sustainable and over time the walls will slump (fail) to the lower angle of repose you see for the overall deposit. When this occurs the floors of the channels will be filled with the slump material.

In the meantime, when more rain falls, the runoff will naturally flow in the extant channels - the water taking the path of least resistance. The water will flush out the loose slump material and if the force of the water is great enough it may also widened the channel and eventually cause more material to slump into the channel.

A material's angle of repose is a function of its cohesion and it is the overall/average angle the material lies at over a long period of time.