Just a few thoughts to make the plows more valuable and useful and to make farming more enjoyable and skill gain reasonable.
Perhaps you could make the plow able to make 'soil' into 'fertile soil' , not just grass into plowed soil. And/or perhaps based on skill, the plow could raise the quality of soil somewhat.

In its current state, the plow is good to make a large scale field for the first time and then is done. If used to level up advanced farming, it would require hundreds of tiles to be plowed. Usually by the time someone can make and use the plow, you already have at least some fields, so it feels very limited in it's usefulness currently.

However, retilling the ground and turning over fresh soil is the basis of farming, so those adjustments would be realistic as well as beneficial in game. It would also be an option for someone who did not have enough dung on hand or could be used in conjuction with that method.

Also in the game's current state, one can 'pour fertile soil on the ground' and it will be plowed and ready to go. Perhaps you could delete that option so that one cannot make a fertile, plowed field simply by dumping dirt out of his pockets. perhaps have dirt and plowed soil be different?

Perhaps you could set plowed fields to degrade quickly back to grass when nothing is planted in it, and perhaps allowing that to happen could even slightly raise quality, mimicing the practice of letting parts of a field lie fallow, to keep from taking all of the nutrients (quality) from it and allowing it to build itself back up (raise its quality)

Just a few ideas to make farming more immersive and the poor plow more practical.