That would be a variant of letting the land lay fallow - the system followed by the Southern planters of the early-mid 1800s.

But yes, basic crop rotation was not cutting edge - three-field rotation had been practiced for nearly a thousand years in Europe by that point, and four-field rotation (allowing full use of all the land while maintaining or increasing fertility) for around a hundred years.

But what about the slightly reduced short-term profits from not growing all cotton on the land!? Won't someone think of the slightly reduced short-term profits!? 😭