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@freemo @SpaceLifeForm

I can only answer as far as Japanese is concerned, but I expect Chinese has a similar reason for stroke order. In Japanese, it is considered to be a fundamental part of writing and uniquely defines each character. The main reason for the order though is fluidity. When written correctly, each stroke leaves you (mostly) where you need to be for the next; it aids in writing for both speed and legibility. A hand-written character done in the wrong order is more than not, easily identifiable as "incorrect". This difference is much easier to see when written with a brush or flat marker, but pen, pencil, chalk, rocks, burnt sticks ...they all leave a heavy and light side for each stroke made. The order in which strokes are made becomes even more important when writing similarly to the (not cursive) example @skyblond put above. Writing anything in this style would be impossible to read if strokes were not made in the correct order.