Alright I have some input on this idea if you will have me. Side tangent first however, I don't think personalities should go. It is a part of what makes the game unique.
I never said personalities should go. I just said they shouldn't be the prime driving factor of whether a game feature works or not. Personalities are random/beyond the players' control, and generally invisible in their effects, which means that if players select a character with the wrong personality traits, they'll have no idea why nothing is working as it should.
Basically, it would be something that makes the most DF-literate players who most thoroughly research and understand the game find the game even easier, while frustrating the newer or more learn-as-you-go types of players even further than the game already does.
A dwarf teacher that is skilled enough can take on students for your academy or guild hall. You assign him similar to how you operate your military, you set up a "class" with him at the head and assign him students. So for instance you have a master carpenter, and want him to train 2 students. So you assign him to the "class" as the teacher then pick 2 dwarves for him to teach. Similar to how the military works no with demonstrations the teacher will schedule one and his students attend for the lecture. You assign him a workshop for him to teach at and set up a schedule similar to how the schedule works for the military right now. So you could say this month you teach while this month you do not. You will also select what subjects you wish to teach, the menu will display what is required to teach, such as an assigned workshop, in this case a carpenters shop. Now this would mean while the class is in session the shop could not be used for other orders.
This is massively more micromanagement-intensive than it needs to be.
Keep in mind, students are going to be coming and going from the rest of the world on a frequent basis. What you're suggesting would involve making the player somehow be aware of this prospective student, forcing the player to stop whatever they're doing, and then manually add a new student in... and then that student would presumably leave at some point, and be replaced with new students, again...
Setting up a system where there's simply classes, and any random visitor can get in if they pass some security screening and pay the tuition without player intervention is far less of a headache for players.
Now a headmaster noble could be used to help speed up teaching as he would do paperwork that the dwarf teaching would have to do instead. He could also help manage the time better or even be needed to access this system at all, just like you need a militia commander to even start a military.
What paperwork? What generates paperwork, and what happens if you don't complete it?
Also, you don't need a militia commander to start the military. If you start a military, the first dwarf in will be appointed militia commander.
So this system would mean that it takes time away from other projects that the teacher could be doing like producing doors to teach a class, so slower production ques. But the reward could be 4 new well trained carpenters as the bargain along with additional happy thoughts.
Keep in mind, that's basically useless as a reward for the player. One legendary carpenter is vastly superior to 4 skilled carpenters, as you only have so much wood you need carved, anyway. You're basically asking the player to go out of their way to set up an elaborate training area and manually manage the training of multiple dwarves through a cumbersome menu when the same results could probably be achieved as the game stands right now by just setting up a few extra carpentry workshops, setting up their workshop profiles, and telling them to make more barrels and bins for a few seasons.
Further, the point of all this is to train
foreign visitors, which means they'll be leaving the map.