I have read this analysis several times, and near as I can tell you’re basically saying “if blowing up a stick of dynamite provides x energy, we can just use that same x energy to find all the original bits of that stick and put it back together”.
We're talking about converting hydrocarbons -> CO2 + water (or whatever if you care) and reversing that reaction (or similar, since we may want something more stable than hydrocarbons).
There are already machines which do this (anything that does photosynthesis). We're just going to play around the edges of making the reaction more efficient and/or the results more stable.
If it were so simple, we’d be doing it. Over here in reality, carbon capture remains a difficult and unsolved problem in practice, requiring enormous amounts of energy that is—at present—generally far better put to use replacing carbon-based forms of energy than trying to put the carbon genie back into the oil barrel.
You started with a complex macro object and said it's difficult to reassemble. I noted that the reaction is actually simple, this isn't an information problem.
This is a technology problem, and one we are actively working on. And with the correct technology it is a not a large problem.
Trivial, really.