This Japanese is (just barely) legible and makes for a great example of what the OP is talking about. And since Japanese is a surprisingly popular language for HN posters - if you are able to read Japanese - I challenge you read this: https://imgur.com/a/lse8JR0
It was written by a JP native - using a mouse - but her handwriting is typically this bad so having to write using a mouse only made it very slightly worse than usual.
It made me feel better about my own handwriting. I don't sweat the details at all - writing better than natives might get me minor praise but doesn't really benefit me in the long run vs expanding my vocabulary or learning how to read more kanji by spending less time focusing on writing them. I only write kanji nowadays to help with memorization of new kanji and to make sure I can still write the first few "grade levels" of kanji for how natives learn.