Good discussion between the commenters, so I can be brief.
Inertia plays an important role in politics, but I do not believe that inertia can explain the importance of subsidies to agriculture in rich countries. For one thing, the form of the subsidies has in fact greatly changed over time; in particular, acreage restrictions are less important than they used to be. As someone pointed out, countries like New Zealand have radically changes their approach to agricultural subsidies. So it is necessary to find more basic causes, and the size of the agricultural sector is an important one. Other small sectors also are often successful politically.
I disagree with the assertions that subsidies are needed to keep prices of food and other farm goods down. In fact, the majority of the subsidies, such as acreage restrictions and export subsidies, raise prices to American consumers. The OECD study that I referred to concurs that the majority of the subsidies to agriculture in OECD countries increase, rather than lower, prices of farm goods to consumers.
Is there an important externality to the rest of us from having more people and land employed in agriculture? If so, it is not obvious what it is, especially since these subsidies mainly go to the larger and the more prosperous farmers. That does not prove there is no favorable externality to urban dwellers from farming, but it cautions against accepting that argument easily. People employed in virtually every sector believe their contributions exceed what they receive in pay or other ways, and farmers are no exception.