I think a key point about this, which was only clear to me after I learned to write Hanzi in Mandarin, is that if you write the strokes in the wrong order it will not look right at the end.
To someone looking at characters for the first time, it's not obvious that the stroke order matters to the reader as spelling does in English. It's not about fetishization of the process over stroke order, it's really obvious to the reader if you wrote the character incorrectly.
I've kind of wondered about how you can tell -- do you know of an example that's online anywhere that makes it clear how it looks different? (... when written with a pen or pencil?)
see: す - imagine if it were written from bottom to top. The placement of the 'straight' part of the vertical line and the placement of the 'curl' would be opposite (especially if you're using a brush instead of a pen). This is similar to the lowercase English 'a' or 'u' written bottom to top - especially if using cursive.
or see: お
the last 'dash' in the top right is a retouching of the paper after the curl on the bottom right. Imagine a swirl that starts in top middle, swings around on the bottom left, swings around on the bottom right, lifts off the paper, and then touches back down briefly in the top right. If you're hand-writing, that little landing dot can be huge, tiny, or even conjoined, but to be legible it's generally visually a continuation of the lower stroke. If you just copied the letter without any concept of stroke, it would be difficult to read because you'd be looking for that swirl. Imagine the dot on a lowercase 'i' - it's supposed to be directly above the stroke for your brain to render it as an 'i' vs an 'l'. It's why when written out you can distinguish 'il' and lt' even though they're quite similar if drawn literally, quickly.
An example of stroke order vs stroke direction is more apparent when you need good proportions. Kanji like 風 or 看 are really hard to 'draw' with good square proportions if you don't stroke them in a particular order. Kind of like trying to draw a face by starting with the nostrils, then doing the eyebrows, and ending with the outline of the face - it's tough.
Interestingly, the Japanese hiragana letters are really designed to be written with a brush from top to bottom. The letters flow from one to the next really nicely when written from top to bottom, and are actually much harder to write properly when written left to right. See: す - き - の. They're much more natural to write top to bottom, and keep going down rather than from a left to right (which is also indicated by stroke order - the horizontal bars on the letters above are written before the downstrokes).
Ehhhh. This is all starting to sound rather speculative. People draw the lowercase 'a' in all sorts of different ways and end up with an equally valid result. There's no particular reason why drawing す from bottom-to-top would require that the shape be different. You just have to know the shape.
I also don't buy Emmett's claim. There are regional differences in stroke order, even for hanzi. Japanese people use a different stroke order for kanji than mainland Chinese people use for hanzi, which again is different than the stroke order used by people in Taiwan and Hong Kong. The differences implied by these things are smaller than the differences in CJK fonts, which have no inherent "order" at all, yet people somehow manage to read.
Stroke order matters for calligraphy and memorization and dictionaries, but as patio11 says, it's largely just prescriptive. Spelling is prescriptive, too: it's historically and/or conventionally derived, but knowing the rules makes learning words easier, and you certainly can't use a dictionary without it.
It's not about what can be done, it's about where the ragged edges are, and where the core is. If you put any squiggle in the top of す it will make no sense. But you can do nearly anything you want with the bottom half and it will make sense (like an English 'j'). It's not that the stroke order is sacrosanct - there are indeed a lot of ways to write an 'a' in English. But some of those ways will not be well-read by others. Those regional differences can be really confusing. Ask a french person to write the numbers 1 and 7, and then an American. They are nearly exclusively legible precisely because of their orthographic rules. And yet 'people somehow manage to read'.
The hard and fast rules are prescriptive, but once you start writing, you realize that some of that prescription ends up as description. There really are detectable orthographic differences in how stroke order affects (generally, of course) how people write.
children have penmanship work in the earlier years of learning the chinese language but that stops within a few years. what about all the characters that they pick up after penmanship work ends? there is some intuition to the stroke order that guides the writing of more elaborate characters, that is maybe picked up in the formative years. and the intuition seems extremely consistent among users of the language.
i have not met anyone who did not learn the chinese language without doing penmanship work, and so i cannot say what it means to ignore the stroke order when writing chinese. if one were to pick up the latin alphabet with an unusual stroke order and were to carry that habit to adulthood, will we find his handwriting difficult to read? if he managed to train his hands to write with a most unusual method will he still write perfectly legibly, and can we even distinguish his stroke order if we were to inspect it carefully? i don't know the answer to this. out of curiousity i wrote the alphabet with a totally unfamiliar stroke order (e.g. starting the y's and g's from the bottom) and it looked as if i wrote it with my off hand - unsteady and unpracticed - which seems to suggest that maybe with some effort it could look totally similar. i can believe that without stroke order guidance one could still achieve legible chinese writing.
There are some minor differences in stroke order by region, but the basic rules are always the same (e.g. top before bottom, left before right, etc).
It's genuinely hard to read people's writing if the stroke order is off.
If you write super slowly and deliberately it may not matter much, but in my actual real-life usage I've found that it does. If you're learning, you're definitely better off learning the standard stroke order for the area where you live.
I mean, sure...there's a gray area here. I could theoretically write all of my latin characters from right-to-left, but it would be wonky and hard, if only because english is written from left to right.
I believe there's a reason for the rules and that you need to know them. I think patio11's metaphor is the correct one -- it's a lot like english spelling.
Of course it's prescriptive and there are regional differences. As you say, it's just like spelling. "Colour" still looks wrong to me. Just like a different stroke order looks wrong to a native reader. The point is the differences are visible to the reader, it's not just an arbitrary set of rules for writers. The reader can tell if you're following the rules or not.
I think you're right that there are certain characters where drawing it the "correct" way leads to a better result, and that there's a reason for the rules (i.e. that the rules are rationally derived). Using the correct order is also probably faster. I think the spelling metaphor is a good one.
I doubt your last claim in the general case, and I think the GP comment in particular is taking things too far -- there's no way that the average Japanese reader is going to be able to tell the stroke order used to write ぉ (in handwriting scenarios, not calligraphy), so long as you don't mess up the form of the thing.
It's their culture. There is no Chinese without People making it, and the people who made it say this is how it goes. There can't be a higher or lower analysis of the topic since it exists to be analyzed at all through their efforts to give it meaning.
The blog post's image on a child's struggle is kinda sorta one example. It shows the pencil at the last stroke of the bottom right character and that stroke order is wrong. Correct stroke order is shown here: https://en.m.wiktionary.org/wiki/%E6%88%90
To answer your question, if the image doesn't show the pencil positioned on that last stroke, I'd say that the characters don't look right and may infer but cannot tell for sure that they were written using incorrect stroke orders.
To someone looking at characters for the first time, it's not obvious that the stroke order matters to the reader as spelling does in English. It's not about fetishization of the process over stroke order, it's really obvious to the reader if you wrote the character incorrectly.