My handwriting isn’t very good, and I recently finished university. I avoided handwriting any time I could by typing things out and printing them off as needed, pretty much the only time I had to submit handwritten work was on exams, and for those I mostly just wrote a little slower than I usually would to make it a little neater (enough to be legible by others if they make some effort).

I never experienced exams I did at the university I went to (in the US) being marked off because they couldn’t read it, and I think the TAs that did most of the grading (students from higher years or graduate students) probably aren’t mean enough to take off points from a fellow student just for “bad handwriting.” Whoever was grading my exams was probably annoyed at having to read my writing, but I didn’t really encounter any big problems.