One versus two plies of prepreg?
Having spoken to PCB manufacturers here in the US and one in Europe specifically about this issue, I learned the following:


PCB manufacturers control the final thickness of the finished boards as well as the dielectric layers formed using prepreg compression and resin flow. The finished thickness is important for differential pair and other controlled impedance signal lines.
To be able to control the thickness, they need some resin to be able to flow out. 7628 is low resin content versus 1080 (see Isola technical prepreg resin content specs). Thus, low resin content prepregs limit thickness control.
Higher flow at the laminate interface tends to lead to better adhesion and lower chances of delamination in the subsequent part population (reflow oven).
Modulus gradient. The gradient in mechanical modulus (change in stiffness) also leads to delamination. Two prepregs back to back will have two very clean prepreg surfaces back to back that bond very well. The difference in modulus between the prepregs and the already cured core is then spread out over two layers of prepreg instead of one. The adhesion between already cured core and prepreg is typically lower than prepreg to prepreg (especially when prepregs are same resin system, CTE, and glass matrix).
Cost: 2 layers costs customer more. 1 layer costs manufacturer more in requiring more engineering time/tighter manufacturing control. 


My experience with this issue is in replacing (2 x 106) construction with (1 x 2113) or (1 x 2125). 106 is the most expensive prepreg and highest resin content. 2125 is more common in Europe evidently but similar thickness and usage to 2113. I have heard there is at least one manufacturer that uses 1 x 2113 (external single layer 2113) construction as default or standard construction but have not found it yet. 

From contacting Isola, (core and prepreg manufacturer), I learned the 2113 laminate was actually developed over a decade ago (pre 2010) specifically to replace the usage of two prepregs in some constructions.

I have been designed circuitboards for 20+years from 2 to 8 layers.