For the following the sims to school thing, I think EA would need to be careful not to make it just staring at your sim sitting at a desk all day. Yeah, things might be more fun if you're controlling a more unruly student, but not everyone is an unruly student. If they found a way to make it compelling even if your sim is behaving properly (things like answering the teacher's questions, asking your own questions, raising your hand to comment on the class, etc.), I would like following the sims to school. Otherwise, I'm not sure I would.
Having a lot of interactions would certainly help. Maybe one sim spends the whole time doodling while another is passing notes, or someone spends the time daydreaming (raises fun while decreasing any gains from the class, maybe?).
The strengths and weaknesses thing is a cool idea and I'd love to have more ways of distinguishing sims. One concern I have about that is I feel there should be a way to customize those (probably through cheats). If you create a sim specifically to be good at a certain skill, it's going to be really annoying if they randomly get that as a weakness and possibly ruin the story you're trying to tell. If I were to make a sim meant to represent a certain person (fictional, historical, real, myself, etc.), I would want their strengths and weaknesses to be close to their counterpart's. It would be really annoying if a sim meant to represent a socially awkward person got charisma as a strength, or a sim based on a pyromancer
character got a fear of fire.
Perhaps it could be that CAS-made sims don't get any talents or weaknesses, but I would still like a cheat to give them talents and weaknesses if I see fit.
"Talents that influence character values and public image."
That would be really cool. There should be corresponding weaknesses for those too. Maybe for the custom schools, also classes that focus on building those things? You could have a school that focuses more on character values or reputation than skills (and, of course, have a school that impacts them negatively deliberately).
Getting skills or other benefits and discovering talents and weaknesses from school are neat. I feel like adding an extra layer of rewards for schools would be neat. Maybe sims who do really well in school get a reward trait while those who do really poorly get a detrimental trait. And then for the private schools, you can choose from a list of potential reward traits (you can only pick one) and detriment traits (once again, only one) for that particular private school. Perhaps your reward trait choices are limited by what types of classes you chose (sims with As aren't likely to become athletes because of school in a school with no gym class).