Sure, but you are also fanatically pro-EU, and the CAP is not just an EU policy, but the biggest and most expensive one of the lot. As members of the EU, we (the taxpayers) paid not only the subsidies that went to your hated recipients of inherited wealth, but also for the resultingly more expensive food in the supermarkets.
Don't get me wrong, there's a dilemma for all of us in this. On one hand, I don't believe we pay sufficient for our food (6% of income, against more than 30% 60 years ago) to keep many farmers out of virtual penury, and some of their workers both in production and supply chain not far off of slave labourers. On the other hand, affordable and nourishing food must be available to those even on the lowest incomes. I don't know how that circle can be squared, but the CAP is definitely not the, or even an, answer.
Incidentally, even beans and cabbages require farmers (and a disproportionate number of cheap labourers) to produce them.