I wouldn't say it's a hard assumption, it's just mighty convenient that there was a carboniferous period on this planet that left us with some really easy energy to use for industrialisation.

There's a question then of whether we'd have been stuck on a pre industrial ladder rung if it hadn't happened.

It just seems necessary, but of course the opposite might be true, that if we didn't have this easy energy we'd have jumped ahead with solar and wind or others instead.