Description:
1) Select a paint tool (brush, airbrush).
2) Shift-click on one of the following: clone, smudge, dodge/burn or blur/sharpen
You have then a dual brush with the given effect. The effect or texture tool
should be applied first when painting, and the brush/airbrush over it
(incrementally or with a buffer).
The idea is that real painting/drawing tools alter the underlying color and is
altered itself by the background's texture. Instead of adding such features to
the brush tool itself, as it has been requested, why not combine with already
existing effects?

I've put together some quick simulated samples of possible effects:
http://mypage.bluewin.ch/pascal_lsgc/gimp2paint/

I can comment the samples if you want.

Advantages:
I can't stop thinking of some new possibilities this would offer. The most
essential for a natural look are the smudge effect (existing color is "drown" by
the brush as new paint is added) and some texturing which the clone tool does
perfectly well. The multiple options and painting modes for each tool would
allow infinite possibilities.

Problems:
I'm aware there are many questions left (does each tool use the same brush or
can we select different ones, which tools should be allowed...)
I have no idea of the Gimp's internal structures, therefore I don't know if it
would even be possible.
The clone and dodge tools seem not to be "incremental" (I suppose the effect is
drawn in a buffer): are there any priorities issues if the brush tool has the
incremental property checked? Which one would be drawn first?

Tank you all for the excellent Gimp 2.0!

Pascal