Subsidies is a hugely loaded term that would take more than a few comments to even begin to cover, but yes, they do cover those things that you mentioned, but a lot more than that. Heck they even sometimes pay farmers not to grow things at all - we used to get a check not to grow tobacco. I was a child then, I don't remember all the details.
Importantly, subsidies already include a federal crop insurance program that the government pays most of. That would cover most reasons for loss of crops. But there's also payments when say, you had a great year, but prices crashed through no fault of your own. And separate payments for say, farm animals catching disease and dying, or natural disasters. And separate payments for things like the messy situation COVID created. And a lot, lot more.
My comment was mainly with the lens of 'get rid of subsidies and buy your own insurance', and well, we see how well that works with health insurance. "Oh sorry Mr Smith, those cicadas were underground when you bought the farm, pre-existing condition, denied."