It's maybe a stretch to say that without cotton the Industrial Revolution would not have happened. There were plenty of other important things happening that helped it come about: invention and development of energy sources, like steam engines, improved water mills; development of financial markets and legal protections that freed up capital for investment....And coal was being developed ( even though mining stayed a miserable occupation) , and plenty of people were trying to "improve" agricultural food sources, like Jethro Tull and Coke of Norfolk.

Cotton was important, though, in that it responded well to economies of scale at all levels in its production, processing, milling, and sale. Other fibers available , like linen, wool, and silk, required extensive hand labor in cultivation and processing that made it somewhat hard to make them in huge quantities. Eli Whitney's cotton gin made the most difficult part of cotton processing comparatively easy. It was also found that the plant grew extremely well in the US south, had no serious pests or diseases there ( until the boll weevil moved in from Mexico a hundred years later) and could be cultivated in huge quantities using cheap slave labor. This huge supply of cotton coincided with English development of water and steam powered spinning, textile milling, dyeing and printing ( aided much by German dye chemists) and an extensive English trade network to get it to other markets.

And the markets were big: food is indeed important, but everyone wears clothes - as Mark Twain remarked, naked people have no influence in society. And clothes wear out or become outmoded, so even glutted markets don't stay glutted.