A couple of things about this.
First, the average farm size in Iowa may be about 350 acres, but I would guess that the median farm size is quite a bit smaller. There are some big farm operations, and they are going to skew the number up, when comparing it to a traditional "family farm."
Second, I agree that having collateral that you can borrow against is a useful and powerful tool, but I don't think for most of them it's going on, for a couple of reasons. For most farmers, this is the extent of their collateral. If they are farming their land, each spring they need to spend a bunch of money on inputs, and they will almost always finance it because it's not exactly easy to just write a $250,000 check. Then they clear it when selling outputs.
There are certainly farmers who are leveraging the value of the land they own as they try to make their operation bigger. These farmers fall into two categories: Those who are successful in growing their farm into a huge operation, and those who get over extended and end up bankrupt. But these are a very small subset of farmers.
Also, as investments go, farmland has at best a "modest" return. It's a decent hedge against inflation, but....
Take your 350 acre farm. If you rent out the land, you'll get $275-300/acre. From your $100,000 in rent income, you'll have to pay income tax. You'll also have property taxes of about $30,000 or so.
And they aren't going to sell the land because of capital gains tax. Even if no one in the family is going to farm the land, they'll sit on it until they die, then the kids sell it and reap the reward.