I think the Japanese obsession with stroke order has its roots in writing with brushes and slower-drying ink. If you use them, stroke order will affect what letters look like more than when using ballpoint pens.
Happily the rules had relaxed by the time I had to write left-handed, and very messily with a fountain-pen!
(Now she’s seven and in an American school where they don’t seem to care about practicing handwriting at all, or indeed any kind of repetition. Instead the focus seems to be on parsing complex and ambiguous written instructions.)
I love how this almost sounds like a compliment, almost.
We were monitored for correctly pointing the back of a pen directly into our right shoulder joint. If it didn't point there, you didn't do it right. Luckily, we also had a guy who was a lefty, so that was a blasphemy of a much higher order and let most of us, the incorrect pen holders, fly well under the radar.
Then came high school and computers were now ubiquitous. We all switched to some bastardization of typed cursive. Kind of like writing a computer font with more ligatures. Looks like chicken scratch, is hard to read, works okay.
Biggest thing we dropped were all the cursive characters that don’t look like their typed counterparts.
Even when I was in high school, one of my classmates once lost points on a test because he wrote his name in all capitals but dared put a dot on the letter i.
Side note: since you mentioned ballpoint pens, (at least 10+ years ago, things might be different now) we weren't allowed to use a standard ballpoint pen/biro; fountain pens were preferred and micro-point ink or gel pens were allowed.