As far as I can tell this is just a misunderstanding of "growth" in an economic sense. Growth is the result of improvements in productivity, which tend to reduce energy use (per item produced). We consume more energy net because we produce more.

If, eg., products became more expensive because of limited energy (or relevant taxing of externalities) then we would grow more slowly -- we can still produce more through innovation and consume less energy.

It took a huge amount of energy in the past to make a single pair of socks -- today, it takes a tiny amount.

I think the relevant question for 'exponential energy-consumption graphs' is what the relationship is to growth (it simply cannot be assumed that there is a 'deep causal' relationship; this is fallacious equivocation).

Eg., population has been increasing exponentially. Could a static population size produce a flat (or falling) net energy use graph -- whilst still obtaining economic growth (ie., productivity improvements)?