What is it about ancient craton geology that results in associated kimberlite pipes containing economic diamond deposits?
The Science Daily article How diamond-bearing kimberlites reach the surface of Earth: Acidification provides the thrust (Ludwig-Maximilians-Universitaet Muenchen (LMU)) reports of research completed by an international research team led by Professor Donald Dingwell, Director of the Department of Geo- and Environmental Sciences at LMU.

They state that ancient cratonic crust provides silicate minerals that result in the originally basic magma to become more buoyant and as they are forced through the pipes, it causes the buoyant magma to move fast.  With the authors describing that as the magma ascent increases in velocity, the more silicates it gathers (entrains), increasing the dissolved silicate concentration - until the amount of released $\mathrm{CO}_2$ and $\mathrm{H_2O}$ greatly increasing the velocity of ascent, as the authors state 'like a rocket'.

A more thorough geochemical description is provided in the article Kimberlite ascent by assimilation-fuelled buoyancy (Russell et al. 2012), the proposed model mechanism as the original kimberlite melt to be carbonatite-like - poor in silica content, this magma assimilates materials during its accent through the upper mantle and crust, becoming more silicic, causing the $\mathrm{CO}_2$ solubility to decrease, reducing density and increasing buoyancy, causing the magma to accelerate.

In terms of why cratonic crust is the locale of many diamond rich kimberlite pipes is described from Professor Dingwell as being due to the silica rich cratonic crust is thick enough to provide the magma to make contact with the silicate rich minerals therein.