I'm a tech writer, and I agree. The problem with "they" is that using it as a gender-neutral pronoun is gramatically incorrect, so it doesn't work in formal or professional settings. "He/she" is clunky, and while writing to avoid pronouns altogether sometimes works, dancing around it can also result in clunky writing. Having said that, since "they" is becoming common in everyday use, formal English may soon evolve to accept that form of the word.
Style guides tend to address the issue by saying "just be consistent with which pronoun you use", which makes sense to me. But I also agree with OP in that if you're writing an example, you're totally free to write a hypothetical female character instead of a male one, just to break up the habit of assuming everyone is male. Writing examples that sometimes use male or female characters isn't unusual in instructional writing. Going "Jane decided to do this" in one example and then saying "John decided to do this" in a later, unrelated example is fine, and not confusing to the reader.