Your example only holds if you assume the only form of rebound is a specific indirect rebound mechanism, which is knonwn as the "re-spending effect," wherein energy savings are spent on a general bundle of consumer goods, which then have the average energy intensity of the economy as a whole. (For a taxonomy of rebound effects, see here). Indeed, no one predicts indirect rebound effects to add much more than another 5-15% on average to the overall rebound effect, as I wrote in my extensive 2011 review of the rebound literature.
What you are of course ignoring is the direct rebound effect (as well as several other indirect mechanisms), wherein an improvement in the efficiency of an energy service reduces the apaprent cost of that service, triggering an increase in demand for that service. Now where energy services are concerned, of course they are much more energy intensive than the economy as a whole. So if we make lighting (about 70-80% energy cost to total cost of lighting ratio BTW) or a blast furnace at a Chinese steel mill, or freight trucking, or an industrial motor at a factory more efficient, direct rebounds in energy demand can be far more significant than the overall energy intensity of the economy indicates. That's why the literature on each of these cases shows much larger rebounds than you want to acknowledge.
And again, the fact that energy is a relatively small share of total US GDP does not at all imply that rebound effects are small. If energy expenditures are 8 percent of US GDP, and we make all energy services twice as efficient over the next 20 years, as in your example, then that implies we just made 8 percent of the US economy twice as productive over 20 years. That would grow the U.S. economy by 4% over that 20 years, or 0.19 percent per year increase in U.S. economic growth rate over those 20 years, if we assume these gains scale smoothly. Now that would be a nice welcome boost to U.S. GDP, but two orders of magnitude less than your "simple" (and flawed) example above.
Now what does that mean for the scale of rebound? Well let's assume for sake of argument that we are in a rich nation like the U.S., so direct rebounds are in the 20-70 percent range we see across empirical studies for the U.S. (see links in my original article). Let's use 50 percent as an easy middle of the range figure for the average rebound. In that case, instead of shrinking to 4 percent of U.S. GDP, energy expenditures would only shrink to 6 percent, as half of our energy savings are eroded by direct rebound. Then if the economy as a whole grows by 4 percent and we spend 6 percent of GDP on energy-related expenditures now on average, we would spend an additional 0.24 percent of our original, pre-efficiency GDP level on energy. That would erode another 6 percent of the expected total energy savings (0.24 percent of GDP / 4 percent of GDP original energy savings = 6 percent of original energy savings). Our total rebound in this case would be 56 percent.
That's a lot of multiplying percents, so go ahead and check my math, but the logic there is sound, and corrects the clear errors in your simple attempt to disprove the possibility of very large rebounds.
Now transplant this case to the developing world, which is less efficient, and where energy use is more like 12 percent of GDP. Say we get 50 percent more efficient there as well over 20 years, leading to a 6 percent increase in GDP over 20 years, or 0.29 percent boost in the growth rate.
Now let's assume direct rebound effects in the developing world are closer to 75 percent on average (again see evidence discussed in the original post). Then instead of cutting energy expenditures in half to 6 percent of GDP, we lose 4.5 percentage points of that savings to direct rebound (6 percent * 0.75), and we wind up still spending 10.5 percent of GDP on energy. With GDP now also 6 percent higher, the indirect rebound from this macroeconomic growth and respending is 0.63% of our original GDP or an indirect rebound of 10.5 percent of our original energy savings (0.63 percent / 6 percent = 10.5 percent). Total rebound in this case is north of 85 percent.
These are all hypothetical, rebounds for very large, economy-wide efficiency improvements. Of course the sector and country-specific cases will differ. But I hope you see why the small share of the economy spent on energy in no way implies that rebound effects are small.
Your continued insistance that they must be small, despite mounting evidence to the contrary, as well as the admonishions of the IPCC, is unfortunate. As I noted above, the evidence does not support the idea that backfires are the norm. Nor are they impossible or even particularly rare. My 2011 review of the literature made that quite clear.
However, the evidence also pointedly does not support the idea that rebounds "where they are found, are quite small," as you claim. As my original article notes, rebounds in the 35-80 percent range are still a very big deal for energy planning and climate mitigation. Please stop trying to imply otherwise.
Finally, your claim that the evidence for rebound effects is not empirically grounded or is based on non-testabable hypotheses is belied by the massive amount of literature on the topic. Just search Google Scholar for "rebound effect, energy, empirical" and have fun reading the reams of papers on this, which you seem to have completely missed...
I suggest you start with these three recent examples: