There are many reasons why the government should not (we can argue) provide subsidies for farms. Let us look at the two most important.
First of all, there is the argument based on economic theory. Classical economics argues that the government should not subsidize any industry. If American consumers want the things that American farms can raise at market prices, they will buy those things. There is no need for the government to intervene. If the farms cannot raise things that people want at prices they will pay, the farms should go out of business. This has happened to many other industries in the US and there is no reason that farms should be any different.
Second, these subsidies were largely designed with the idea that the government would be supporting family farmers. Today, family farms are not the dominant model in the agricultural sector. Instead, agriculture is dominated by agribusinesses that do not need to be subsidized. There is no reason to provide subsidies to large companies that are easily able to take care of themselves.
Therefore, the idea of farm subsidies is bad economics (we can argue) and is rooted in a vision of an America, dominated by family farms, that no longer exists.