Actually I do spam trading posts in my puppets, since they're on a gold focus anyway. Most puppets you get from AI will more often than not be spammed with farms, which can get expensive in happiness because they'll grow so big. So I went and replaced most of them with trading posts. Besides, trading posts eventually gives science as well.
The AI actually knows how to do this now, it won't do it before most if not all tiles on your good cities are worked, but it will show up on recommended tile improvements, which means that it will flip them, but since a lot of people who do automate also disable the AI's ability to change improvements, you'll never see it.
Like I said, I'm just playing devil's advocate here, I don't automate myself unless it gets into late game of a game I have in the bag with a ton of cities, however I'm reading posts here from people way too confident of their ability to manually control them.
The only real advantages you can get now since it largely doesn't do really stupid decisions (since they modeled it after what we did in Vanilla and is still true).
The AI has a small laundry list before it might get to things like:
Mining hills when you want production faster than growth.
Cutting down a forest for an instant hammer boost for early wonders. (it doesn't touch em really anymore except for Lumbermills)
Not putting a plantation on a Banana. (I've noticed however that this shows up much lower on the list, so you might not see it either, it won't touch them if you got a University in the City)
After Economics it can sometimes favor Trading Posts on hills you might have otherwise mined.
Everything else it does reasonably well now. It favors Strategics and Luxuries. It won't go city hopping too much unless there isn't a worker near a strategic/luxury in another city. It connects cities at appropriate times.
Anyways... On Emperor or below, you won't lose because you decide to automate workers (you'll lose to the ton of other decisions you did wrong) It might be a good habit to pick up, but when someone comes in here who doesn't even know how to micromanage citizens, you are almost wasting their time trying to tell them that auto improving is bad.
I think there's one or two posts that are saying the AI are terrible at it because of it. Even one boasted that when he takes over a city. He thinks the AI's improvements are always terrible. I haven't seen much or any of this.
Post screenshots of what you are saying. Firaxis often reads these. They can look at them and keep improving the worker AI.