Chase the niche, not the average. Imagine some situation which has highly specialized demands upon it that are outside of the everyday, and you'll get something much more interesting. Here are some ideas do get your creativity flowing.
Most writing systems are based upon the documentation of a spoken language between people. But, what kind of writing system would you develop to record American sign language, or dance routines, or to systematically name plants, or describe astronomy observations? What if the purpose is to write down bird songs or insect chirps? What if the primary purpose of your writing system was to accurately describe human faces in a standardized way that was good enough to walk into a bar and pick out the right person from the description? These specialized writing systems could become universal in the way that the main system for writing down music has become today.
Eventually, those languages might even develop more general uses and become full fledged general purpose writing systems. The earliest writing systems from Serbia to Egypt to Pakistan weren't developed by poets or historians or priests or academics. They were developed by accountants, ration system bureaucrats and traveling merchants, mostly to keep track of connections between goods and people. Eventually, the accounting symbols were generalized for wider use.
What about a writing system designed for writing with your toes, or blinking your eyes at a computer, or having a computer user interface that tracked your eye movement, or with a stylus in your teeth, or that you would lick onto a surface, or claws, or that would utilize a prehensile tail?
What kind of writing system would be well suited to a sentient species that lived under water like dolphins or whales or mermaids?
What kind of writing system would people raised in China but never formally trained to read or write in any language develop?
What about a writing system that uses three-dimensional instead of two-dimensional characters? What about a writing system that maximizes information density by utilizing color, texture, thickness, orientation, and relative position context as well as character shape to convey meaning?
Why settle for one writing system for one language?
Japanese has four! (logographic kanji, which are adopted Chinese characters; the Latin script (rōmaji), syllabic hiragana, used primarily for native or naturalised Japanese words and grammatical elements, and syllabic katakana).
English has cursive (with upper and lower case), print (with upper and lower case), shorthand for certain specialist writers, and a small number of logograms (e.g. @ $ & #).
Urdu and Hindi are basically the same language, but in different scripts.
Some writing systems cross linguistic boundaries. Both Japanese and English share systems for writing music and mathematical and physical symbols, including recent writing system inventions like Feynman diagrams to summarize interactions in particle physics. Could a more efficient way to describe genetic code in writing be developed? What sort of writing system might an international system of notation for prostitutes develop? What about a notation system to describe personalities or to summarize interpersonal interactions in small to medium sized groups of people? What sort of writing system would surveyors in a place where nothing came in straight lines and nothing was on flat land develop to write legal descriptions in?