Calligraphy is one reason and the pen handwriting is another. Daily handwritig is done mainly in semicursive and cursive styles, if the stroke order is not set, or mistaken, it would be impossible to read the text which is already rather complex (especially in 草書 - cursive style). Aesthetical values are another issue. Kanji written incorrectly look like decrepit creatures from X Files. Lastly, learning kanji and radicals would be the third reason. So, if you are serious about learning and understanding the Chinese characters, you must learn the stroke order, which is not that difficult.
I wrote you some examples:
1. Kanji 栽, meaning plant (same as in bonsai - 盆栽) Pay attention to the stroke order in the left hand side, and then the change of it in the right hand side (stroke order change is permitted in cursive script, but also there are strict rules to it). Without knowing the proper stroke order you would not be able to write it, or even read it.
2. Kanji 心 meaning heart. You have shown here not only the stroke order importance but the overal balance issue as well. Both need to be taken into consideration while learning how to write by hand, be it a brush or a pen.
