Having good handwriting is as important as having good pronunciation.
Why?
When you’re communicating with someone, their minds should be focused on the content and meaning of what you’re saying or have written.
They should not be consciously trying to figure out what words you’re trying to use.
That effort should be entirely subconscious, which means that what you are saying or writing should be in a form that the subconscious mind and the pattern-matching parts of the brain have been trained to expect.
Just as the tongue position when speaking Mandarin is completely different than the tongue position when speaking English, the techniques and stroke order when writing Chinese characters are also very different than those used when writing English.
If you use Chinese patterns and stroke order when writing English, things will look very strange, and the person reading what you have written will have to waste conscious thought interpreting what you have written instead of thinking about your meaning.