Or, in other words, was there any genuine US government policy of the 1930s that would result in anybody receiving monetary compensation for refraining from growing a crop? And was it really lucrative enough that somebody would do what the character is described doing, and buying up as many acres as he can lay his hands on in order to not grow Alfalfa on those too?
Yes, this was a real government policy from the 1930s directed by then-Secretary of Agriculture Henry Wallace, known as the Agricultural Adjustment Acts of 1933, 1936, and 1938. Government incentives to reduce agricultural production had two intended effects:
The Great Depression was caused in part by a collapse in agricultural commodity prices brought on by oversupply generated by (1) strong harvests and (2) reduced demand for exports overseas. Furthermore, those strong harvests were generated in part by aggressive plowing methods on the Great Plains which depleted the topsoil and amplified drought conditions occurring naturally at the same time in the early 1930s. Thus in the interest of protecting farmers' ability to sell goods at self-supporting prices and to keep soils from becoming overly depleted in rushes to out produce one another, the government did indeed pay farmers to not plant crops and keep their land fallow. In 1938 this was expanded to where the government would guarantee the purchase of farmers' overproduction, and then distribute it as food aid (this is where the notion of 'government cheese' arises from). But these policies are most frequently discussed in the context of corn, not hay.
While this was popular in the Midwest where many farmers owned the land they worked on, early iterations of the program had negative consequences in the south, where ownership and work on the land was split on the basis of race. As the article Henry C. Wallace and Henry A. Wallace as Secretaries of Agriculture: The Importance of Presidential Support by Per Magnus Wijkman notes, "The AAA had severe social consequences in the South. Sharecropping was common there, so the application of the AAA meant in these cases that the landowner, usually White, effectively got the government payment for noncultivation of the land he owned, while the sharecropper, usually Black, who cultivated that land was effectively dismissed. This led to a conflict within the AAA". This was later (partially) rectified with additional social support programs for displaced sharecropper farmers.
These policies were largely ended under Earl Butz when he was Secretary of Agriculture from 1971 to 1976 under Richard Nixon and Gerald Ford. Under notions such as "get big or get out", Butz called upon farmers to plant commodities like corn "from fencerow to fencerow" and increase productivity without regard for the prior factors in order to seek out international exports in particular. The implications of this have been widely discussed, and range from the increasing consolidation of farms in the US, the 'dumping' of excess production internationally at below local prices (causing similar price issues elsewhere with excess supply), the influx of corn-based products in virtually everything, adverse impacts on the environment, and the role that federal agricultural subsidies play in supporting this whole system -- some of these questions come pretty close to the 20-year rule, so I'll stop there.
Edit: added a new paragraph about implications of the AAA for landowners compared to tenant farmers, plus some grammar
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