For starters, why wouldn't they add children? Because you wouldn't put them to use for RP purposes? That's pretty egotistical, but okay.
Make false assumptions and jump to conclusions much? You hypocrite. If you've listened to ANYTHING M'Aiq has EVER said, you'd know they won't put something he talks about into the game. So it's not my "ego," but rather Bethesda's "ego."
Seriously, though. If there's one thing they've taught me that was worthwhile in science class, it was "NEVER MAKE ASSUMPTIONS!"
Secondly, there's a reason for the Arcane University in Cyrodil. It's a university of the arcane. You would, in fact, need schooling to take advantage of your magika. That's what "knowing magic" is all about.
Call me crazy, but can't you be a mage without joining the AU? It's all about the inner focus. You don't need a school to get in touch with magic.
I'm not entirely sure why you're so anti-children/schools.
Why would we need one? I'd accept one if there was a reason for it. Nothing to really RP about with a school... you might choose to be a teacher for your career, but that doesn't sound very pleasant. What would you do if TES got a school? Would you go inside and watch all the children staring at you because some weirdo just randomly walked into their school? You can't add a school just because you can, with your only reason being "it's nice to have one." I'd say burn that school down and put a cave full of goblins there. Maybe put a Daedric shrine there. Heck, I'd say put in another support for my gigantic house that looms over the city so it doesn't fall down.
Now, if there were to be some reason, any good reason, I'd second-thought myself. But this isn't about me, it's about your fantasy. What would you do in your fantasy world with your fantasy schoolhouse? Nope, not my fantasy, not our fantasy, just yours. What would you do with that schoolhouse?