OP has the right idea, albeit slightly incorrect on the agricultural details. Rotating crops isn’t just a matter of soil nutrition (some plants use more nutrients than others, but they’re pretty much all going to use those same nutrients, even if legumes–nitrogen fixers–can pull some nitrogen from the air and leave a bit of it behind afterwards, which is why the second point was made with planting a cover crop to use as green manure, assuming your soil moisture reserves are adequate enough for that, but what’s left behind will not be enough for the next crop; ‘fallow’ is typically reserved for not planting anything–weeds holding the ground in place–or just tilling the field, which has fallen out of practice because soil erosion is a thing). Farmers need to fertilize to replenish those lost nutrients, just like you, as a writer, might need to take a break and find some inspiration–whether in canon, other fanfiction, or something entirely unrelated–to help get you excited about your fic again and get some new ideas rolling around to help you through the rough patches. Does a particular scene seem really weak or forced to you? Might be a nutrient deficiency, a lack of one element which is limiting the rest from reaching its full potential; try to evaluate the scene with different eyes–say, how another character might view the scene–to see if you can spot ways to improve it, or call in someone your trust for a second opinion.
Crop rotation also aims to prevent disease and pesticide (chiefly herbicide) resistance. So, by giving yourself permission to rotate, your writing doesn’t become stagnant, stale, forced. If you don’t, it might start to rot, getting to a point where you aren’t happy with anything you’re writing and you’re rewriting scene after scene. If you keep pushing it, you might find yourself with what feels like insurmountable writer’s block, where nothing seems to work (like herbicide resistance). Try something else. A different story, a different fandom, however far you want to go. The situation may not look as bad when you come back to it.
…from the fandom feedback perspective, you could liken that to crop prices. Some fandoms tend to review more than others, and farmers keep in mind crop prices when they’re deciding what to plant because they actually need to make a living, so even though it’s not the determining factor in what you write, jumping to something where you’re slightly more likely to see feedback/get encouragement might help your opinion of yourself.
Don’t forget environmental influences, either. Going through a drought? That’s okay. You can’t really do anything about that other than pray for rain and give it time. Inspiration isn’t really something you can force. Flooded by ideas and overwhelmed? Jot down detailed notes so you can revisit them later and just work on your favourites for now. Patchy field? See if you can figure out why. Isolated scenes that need small, intermediate ones to connect them? Scenes that are there but just need to be fleshed out? An attempt at foreshadowing or another literary device that just seems confusing in hindsight? Step back, look at it as a whole, and decide if you need to reseed–rewrite–or if you can just flesh out a few scenes to help the story grow.
Farming is a gamble. You put in a lot, and you have no guarantee of getting anything back in the end. Writing is a gamble, too. It’s hard to share your work with other people, even strangers on the internet. You don’t know how anyone’s going to react. You don’t know if anyone’s going to leave you positive feedback. You don’t know if anyone is going to appreciate all your hard work. But you took a risk to create something beautiful on the chance that someone other than you will appreciate it, and that’s wonderful.