It wasn't important in this case, but my brain kept flipping back to the previous item to make sure I hadn't made a mistake in reading. Ordinarily it is pretty important to the narrative.
Typically in older literature "he" has been used as the neutral pronoun when gender is unknown or unimportant. I've seen a more recent movement towards use of "she", but I don't think I'd say it's "traditional". Am I missing something?
The Chicago Manual of Style does say "he" (though they prefer "he or she").
My personal preference is for singular "they", for what it's worth.
Edit: My version is equivalent to "a preposition is not an okay thing with which to end a sentence."
The relevant concepts here are preposition stranding and pied-piping. These are not "mechanical transformations" in the sense you mean -- there are certain constraints on when a preposition can be pied-piped and when it can't.
"Bill is over there. He is playing with his toys."
"If your child is in the kitchen, make sure they don't touch the hot stove." vs "If your child is in the kitchen, make sure he/she doesn't touch the hot stove."
For many readers the he/she breaks all flow the sentence had.
[1]: http://en.wikipedia.org/wiki/Singular_they
EDIT: s~he/she don't~he/she doesn't~
In the context of the article[0], other options exist like:
If your child is in the kitchen, make sure he doesn't touch the hot stove.
If your child is in the kitchen, make sure she doesn't touch the hot stove.
These sentences are no harder to read than if "they" had been the pronoun used.
[0] - and I really think what the author is trying to do is make the reader think of a different child with each bullet point. Not a single, unspecified four year old, and not a collective group of every four year old, but one unique four year old for each bullet point. Alternating the gender of the pronoun creates this effect.
"If your child is in the kitchen, make sure she doesn't touch the hot stove. If he does, however, ..."
Even when the switch isn't that abrupt, if someone is switching between he and she every few paragraphs, it can become very distracting. Using singular they solves this problem.
Each bullet/item in a numbered list is a new context.