The hard part of writing is content--not syntax.
Just like programming is about logic, and syntax is a minor nitpick one needs to know.
But I think the real reason these rules were emphasized so much is that they are easy to grade and explain.
Many students can’t get the basics down — and their writing is borderline illegible. How are they supposed to master content when they can’t master form?
The occasional mixing up of "its" and "it's" (or even "you're" and "your") really isn't the major problem; this rarely causes confusion or makes text flow bad. Even though it looks sloppy in professional writing, it's fine in a great many contexts.
One of the so-called "illogical" examples is "Walking back from the village, my wallet was lost", because apparently "Does your wallet walk?", and the the "correct" is "Walking back from the village, I lost my wallet", which is basically the same sentence for everyone because no one was confused about a walking wallet in the first example (I personally don't like either by the way, and would write "I lost my wallet while walking back from the village").
Good writing is mainly about whether 1) text reads and "flows" fluidly, and 2) if it gets the point across. My main trick to get this right is to read things out loud in my head, but there are probably other ways, some of which may be better. It's certainly not about boring spelling details or personal preferences.