[ibejoeb]

I agree with you for the purposes of colloquial speech. However, this is formal, and the formality serves a specific purpose.

Somewhat tangentially, we're talking about UK services, and you're citing American style guides. The major British style guides advise against singular "they."

Since we're talking about usability and accessibility, I'm going hammer on the point that this needs to be accessible at baseline reading comprehension levels. Singular "they" is generally not taught either in primary or ESL environments. If it does become part of standard education, we still have generations of people who have not experienced it.