I am interested in some empirical insights that would help verify the hypothesis that farmers don’t like being dependent on CAP direct payments, as they would prefer being able to live off their productive activities alone.
The hypothesis that farmers don’t like being dependent on CAP direct payments seems superficially attractive - after all, farmers are reputed to be individualists.
Since your question intrigued me, I made a brief search for corresponding literature. It yielded no direct hits. Considerable attention has been devoted to CAP-related questions, but no one seems to have published work on whether EU farmers would prefer Smith's invisible hand to CAP.
A characteristically sardonic Economist article from 2005 entitled "Europe's farm follies" focuses on the French experience. It provides useful, though dated, insight into the enormously uneven distribution of CAP payments among member States and within member States, among rural industries and within the same. To quote a brief passage:
Over a quarter of payments go to just 5% of farmers, according to the Groupe d'Economie Mondiale (GEM) at Paris's Institut d'Etudes Politiques. It calculates that the biggest 30 farmers—among them, Prince Albert of Monaco—get an average of over €390,000 each a year. That is 217 times the average received by the 180,000 or so smallest farms, which make up 40% of the country's total.
Research into the question of farmers' preferences evidently would require a highly differentiated approach in order to be meaningful. Prince Albert might consider the burden of accepting substantial CAP payments as a form of noblesse oblige — or perhaps his rural business model simply would not be feasible without CAP. By contrast, market gardeners reportedly tend to receive no, or only minor, CAP payments. CAP recipients apparently constitute a population in which the mean is apt to be meaningless.
Supposing you were to survey farmers and found, for example, that 65% were favorably disposed to the idea of operating in free and undistorted markets in agricultural products. How many of them (other than Prince Albert) would understand that tariff and non-tariff barriers, including deliberate geopolitical dislocations, are holding back a flood of cheap agricultural products from Africa?