While it's true that plants like ferns, mosses, and fungi reproduce using spores, the term "sporophyte" refers specifically to the diploid generation in the life cycle of these plants. This generation produces spores through meiosis, which are then dispersed and develop into a haploid generation called the gametophyte.
So, while "spore-producing plant" is a common phrase, "sporophyte" is the more precise botanical term for the plant itself.