Something else occurs to me: if I was on the SC, when picking a new Warden of Demonreach, I think, everything else being equal, I'd want a middle-aged Wizard. Someone old enough to have learned a few things and shown stability and trustworthiness and so on, but at the same time, someone young enough that he can serve for a long time. Someone young enough, too, that if he does go off the rails, he's relatively manageable to deal with.
If you can find a good candidate, you'd probably want to keep him in place for a while. Making an SC member, or someone that age and power level, might well mean that he can only serve for a century or less, and if go south he would also be a handful to take out.
(Langtry was able to hold off an entire army with one ward, by himself. Ebenezar can shake continents with quakes and eruptions. Rashid is Rashid. Klaus once stopped an entire German military force with a toy duck, IIRC. Imagine that kind of power combined with THE Wardenship and it went sour.)
From that POV, Harry would seem way way too young (and he is!), but a fellow SC member would look too old and powerful.