A nice example of Japanese stroke order mattering are two of the katakana, ツ and シ. The difference is that the former starts at the top left and the strokes move right, then down and across to the left. The latter starts at the top left and moves down, then up and across to the right. It can be hard to tell what one you are looking at in practice if you don't know this.
I think cursive used to serve the same function, which I basically conjecture from the fact that older people tend to be significantly better at reading cursive than me.
Your oldies are better at reading cursive because cursive used to be read and written much more than it is today. It was the fastest way to write, and people had to use it a lot.
Typewriters first and computers later removed a massive amount of handwriting. Schools in some countries reacted by dropping cursive altogether, probably because they thought the effort to learn it was not worth it anymore.
Also, thick-inked ballpoint pens greatly increase the amount of pressure required to write. Cursive is faster if you use a fountain pen or a quill, but disjointed writing is faster with a regular Bic. If you've never tried one, a rollerball pen like the Pilot Precise V5 (regular or retractable) is much easier to write with because it uses fountain-pen-like ink.
I've taken a dive into the world of shorthand. Another thing near killed by computers. Surprisingly fun to get into, though. (The ridiculous sexism in many of the books is cringe inducing...)
I learned just the letter-forms (no shortcut / brief forms) from Teeline Fast, really helped me when taking sermon notes or wanting to write in my journals with a bit of obfuscation.
It helps with that if done right, but you can also reduce ink blotting in block if you learn the right strokes. I've seen a lot of people write block with a cursive a for example, and I think that reduces blot.
And yet on a screen like this there are no strokes, and thus no order. They're shaped differently, but there's no way to tell what order the lines were originally drawn in.
The problem is, if you write by hand and you start writing really fast, you will distort the image. As long as you use the common stroke order, that distorsion will stay readable as it is a distorsion that people are familiar with. Use the wrong stroke order, and your letters will become undreadable at high writing speed.
I'd assume this is the reason why japanese calligraphy [1] is still readible to the skilled reader albeit the images having no obvious resemblance to the original characters
I think cursive used to serve the same function, which I basically conjecture from the fact that older people tend to be significantly better at reading cursive than me.