Author makes a good point. "1700s" is both more intuitive and more concise than "18th century". The very first episode of Alex Trebeck's Jeopardy in 1984 illustrates how confusing this can be: https://www.youtube.com/watch?v=KDTxS9_CwZA The "Final Jeopardy" question simply asked on what date did the 20th century begin, and all three contestants got it wrong, leading to a 3-way tie.
Logic is in short supply and off-by-one errors are everywhere. Most people don't care. I think it's more doable to learn to just live with that than to reprogram mankind.
Imagine, for a moment, that AP adopted the OP's "don't count centuries" guidance. An enormous share of English-language publishing outfits would conform to the new rule in all future publications. Within a couple months, a large share of written media consumption would adopt this improved way of talking about historical time frames.
The best part? Absolutely no effort on the part of the general public. It's not like the OP is inventing new words or sentence structures. There's zero cognitive overhead for anyone, except for a handful of journalists and copywriters who are already used to that kind of thing. It's part of their job.
I think a lot of people take these sorts of ideas to mean "thou shalt consciously change the way you speak." In reality, we have the systems in place to make these changes gradually, without causing trouble for anyone.
If you don't like it, nobody's trying to police your ability to say it some other way - even if that way is objectively stupid, as is the case with counting centuries.