There is no evidence that there would be far less farm fields without that. Farm fields exists if there is profit to be had. Right now the demand for biofuels are directly competing with the demand for animal feed. Farmers will primary grow and sell crops based on what pay the most, and can easily switch if one pays more than the other.
https://ageconsearch.umn.edu/record/360637/?v=pdf The Impact of Market Prices on Farmers' Crop Choices in Ghana https://www.researchgate.net/publication/373480516_Farmers'_... Farmers’ risk rating and crop portfolio choice in Kewot Woreda, North Ethiopia https://www.sciencedirect.com/science/article/pii/S0308521X2... Understanding factors influencing farmers’ crop choice and agricultural transformation in the Upper Vietnamese Mekong Delta
Notice that none of those says that farmers would not use the fields if the current most price worthy crop would go away. Farmers choose what to farm based, among other things, the market. If you remove animal agriculture, you don't get far less fields. You get fields with a different crop in them.
The only thing that will stop farming is either if the external cost of farming is applied, such as pollution, or if climate change makes farming the land unprofitable. Currently that pollution is not applied as a cost. A carbon and water pollution tax could be a strategy that addressed this, and would impact all farming regardless of crop. If that is "perfection" and "enemy of the good", then the definition of perfection is not shared.