I really like this idea. I don't have much time for gaming anymore, but something like this would be a selling point for me. I could write such a game off as an academic exercise.

There are a lot of AI/ML techniques you'd have to know or become familiar with. I imagine the competition to build the best bot at any given task, or best all-around bot, would be quite intense.

Someone please make this game.

Agreed. I don't really play games anymore, but this is something I'd do. Also, I'd imagine it's possible it'd help the companies with things like their bot detection schemes.. the checkbox gives them something of a control group.

Having actually played games where bots are not allowed, I have done both of those things or similar (killing bots, making them get stuck in loops, getting the killed, teleporting them or otherwise making them get stuck, .. just about anything to screw with them) and seen plenty of people doing them.

I do not see how making bots legitimate would really be a factor in this type of behavior.

After the bots are perfected, what will stop users from using them in game along side unsuspecting players?

No one. The developer has not put much effort into fighting bots anymore. And now that the AI is so real, there would be no way they would catch bots gaming the system.