I initially thought the use of circular irrigation devices would be when land is cheap, but after some research I think the main reason to use them is when water is far more expensive than land.

I zoomed in to various areas in the Midwest US, and I didn't see a single use of the circular devices, only square fields which are likely using the linear irrigation device you described.

However, in areas where water is more expensive such as Colorado, I see the opposite: Only circular irrigation devices.

I think what's happening here is that circular devices shoot the water down which causes all of it to land on the crops. The farms in my area generally use a firehose style sprinkler which shoots the water up. This causes a large chunk of water to get lost but it hits the corners of the land. Due to the cheaper water costs in the midwest, this is acceptable.