The only instance where I would concur with this is when you first get the game and have no idea as to what you're doing - you don't understand specialisation, haven't grasped the benefit of counting food surpluses and deficits, and haven't yet come to terms with specialist vs. cottage vs. (insert other) -based economies. Of course the AI barely gets any of this either

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Yep. Pretty much what I think too. The AI does successfully hook up resources in a reasonable order and builds roads in a sort-of reasonable way. The AI does a much better job of this than a brand new player does. Just like you said. I also put one or two workers on autopilot late in the game still - for the rare resources that I just happen to overlook (gems hiding in a newly conquored jungle, for instance).
I still miss a resource simply because I have the resource-finder turned off (it slows down my computer for some reason and it makes clicking on units difficult). The autopilot workers find these late in the game and make up for my Attention Deficit Disorder.
Surely you mean "The AI
does an entirely-horrible job of directing the workers".
Nah. It's not at all good, but it's easily fixable and it's not entirely horrible. Just not nearly as good as someone who actually knows what they are doing would choose.
Agreed!

... albeit rather than let the AI "experience" what works and doesn't work, the player would be better off experience this more directly for themselves.
I agree. For the first games you play, letting the AI run free can teach you some tricks, though. I learned how rivers do/do not connect resources by watching automated workers and clicking on my city to see if the resourece had been connnected to try to explain why the AI would have done such a wacky thing with the roads. It looked bizzare, but when I looked closer, I discovered the rivers-count-as-roads rule for resource connectivity.
Also, if you really can't be bothered to control all of your workers (again, late in the game when you have a ton of workers and an even heavier ton of cities), letting the AI choose what to do is better than fortifying the workers or disbanding them.
In principal, I agree with you. In practice, there are some times (not often and never in the first two thirds of the game anymore) that I think letting the AI take charge is okay.