Just to note: this is not an Ultimaker specific problem... The way I see it... In order to get a relatively smooth surface (tops and bottoms) that layer needs to be "squished" into the previous layer.. when you use a support layer, such as grids or lines, that is not possible, so you basically get the contour of the filament as it was extruded.
To get a smooth layer against a support, the top of the support would need to be flat, but that defeats the ability to remove the support after the model is done. In other words supports depend on bad contact with the model in order to be removable, and bad contact means rough surface.
I've read about dissolvable supports... should we ever get that plus dual extrusion, you'll probably start seeing improvement in surface quality against the supports
In the cases where I need supports, I carefully consider the model's orientation on the build platform. You have to make compromises between surface quality, detail, total plastic used, build time, adhesion.. and probably more -- that's what makes the game fun.