Answer
Short term, the killing of all fungi in the soil could eliminate pathogens, but it would also eliminate formation of mycorrhizae, though spores might allow these to reestablish for several years. Once spores were exhausted, mycorrhizae might be gone for the long term, and soil nutrients would rapidly deplete.
Work Step by Step
Here think about the role of mycorrhizae: they make nutrients much more available to plants. Killing them in the short term has seasonal effects, but they could be permanently lost and lead to very poor soils after a few years.
