The only people who consider switching between "he" and "she" in different examples are internet trolls. Obviously, that's not really true, but neither is your snark.
Look: gender-neutral language in technical writing is not that difficult. Most of the time you can rewrite sentences to simply avoid gendered pronouns, e.g., "the successful applicant will use his skills to contribute to the platform team" becomes "the successful applicant's skills will contribute to the platform team."
As for alternating between pronouns, do you think readers are bothered by switching between using male and female names in examples? If you realize that the first example used Bob, the second used Agatha, and the third used William, do you suddenly leap up, scream INTERNET TROLLS GOT TO THEM!, and punch your monitor? No, probably not. So do you do if you see pronouns switching? Really? Again: I'm betting probably not.
I can tell you that as someone who's done technical writing for a half-dozen companies over the last decade or so that I have never heard of readers complaining about alternating pronouns. I have heard of them complaining about documentation that is exclusively male, though, because it turns out that's something some -- not all, maybe not most, but definitely some -- readers will notice and be a little nonplussed by.