But even within those examples, the energy use per dollar of value generated varies by large orders of magnitude.
A Simpsons SD card uses a tiny fraction of a watt hour for a half hour of entertainment (valued, in theaters and DVD rentals, at maybe $3-5). Watch the same episode on an old-style CRT TV and you're looking at 50 or so watt-hours.
A Google Search uses about 0.3 watt hours to get you the answer you want. The economic value of it varies based on topic, but if you divide estimated total yearly searches (a couple trillion) by Google's revenue ($257B), you get about $0.12. (Note that at average annual U.S. electricity prices, this electricity costs about 1/300th of a cent, showing the profit involved in turning energy into information retrieval.)
A car commuting to work for an hour consumes about 4 kWh (about 200x a laptop watching the Simpsons, and 12,000x a Google Search), but what's the economic value added? Arguably it's economic value destroyed, compared to if we could just live closer to work, because of the lost time and productivity.
That's why it doesn't really make sense to say that 'the "economy" is indistinguishable from "energy" consumption'. There are many things that generate large amounts of dollars and use very little energy, or even save energy. There are also things that destroy dollars and use lots of energy. By equating the two, you gloss over any distinction or ability to make things more efficient.