Whatever form the reformed Council took, it would still have to look a lot like the current one to function at all.
The nasty, inescapable fact is that in terms of magical power, 'are men are created unequal', and all women too. Almost anybody, per WOJ, can learn to do a little magic in the Dresdenverse. It would be a lot of hard work for say 90-95% and not much result, probably not worth the trouble and risk.
The remaining 5-10% or so include your moderate talents, the Kim Delaneys, the Binders, the Victor Sells types, the hedge casters and mid-rankers and a few with some serious voltage. Some of them are super-good at some specific subset of magic, like Mort or Binder, but not so much at the rest of it. Of course most of this 5-10% have no idea of their own potential power and never try to use it or train it. But they could do it, potentially, and some of them could do it enough to be useful if they knew it.
But only a tiny fraction of that 5-10% of the human race is remotely at Wizard level. The WC is made up of several thousand people, but that's out of several billion people in the world. Grant that not every Council-potential candidate gets found and trained. Let's say there are three or four potential Wizards for every one that gets identified and trained. Let's say there, oh, maybe 30,000 or 40,000 people on Earth who could, potentially, become a Council member with the right training.
Forty thousand out of eight billion is one person in 200,000. Plus, that's probably over-generous, there probably are fewer potential Wizards than 40,000.
If you open up the Council to all practitioners, you create an organization that is both too big to function and too weak to do anything, and would inevitably end up dominated by the Wizard-level players anyway. The gap is just that big.
Likewise, the Senior Councillors are already technically elected by the overall Council. But if the Council elects a weak SC...then the Council itself is hamstrung in dealing with their enemies and restraining the bad players among the magical community, too. The Council might reasonably elect a merlin who is not the absolute 100% most powerful Council member, if he had other useful talents or abilities. But they would still need to pick someone in that general ballpark.
The way the WC works arises in much because of the realities of how magic works, and how the supernatural world is organized. A reformed or replaced Council is probably going to end up looking at least a lot like the current one, maybe with some new blood and new policies, maybe some changes on the margins.
I could imagine, for ex, that the Council might permit the larger supernatural community to elect representatives to speak for them on the Council, not full members, but associates of some kind. Things like that. I could see a reformed Council being somewhat more 'open' about its doing, at least among the magical community, more willing to listen.
But it's still gonna have to be the White Council, probably from necessity.
The White Council is fading. They rose to power primarily because of their nearly-unique mix of ability-to-find-stuff-out, ability-to-coordinate (via Ways & other magic-comm's), and logistical advantages. The modern world's Internet can out-info and out-communicate the White Council, and modern transport are a close-second-place for physical logistics. With the exception of a few individuals (not the WC as a whole!) the Wizards simply
haven't kept up. In
The Law, we see Paranoid Gary out-research Bob, regarding a supernatural threat. Arguably, then, the Paranet has already surpassed the WC in some regards; "Information" -- knowledge, data, the relationship between them (and the differences) -- is its own whole (mostly-modern) field of (intense) study, in ways prior generations (including wizards) cannot conceive.
Knowledge, they say,
is power. Harry has hammered on this point repeatedly: wizards (he in particular) can achieve startling victories, by virtue of knowing their foes and prepping ahead of time. WoJ says this is how the WC got to be as powerful as it did (and why being locked-out of the modern info-rich world is, inevitably, sapping that power).
Knowledge is, in fact,
more powerful than raw power. Again, WoJ emphasizes that "punching-match" power-comparisons are largely beside the point, in the Dresdenverse. The one who has the better info, the better prep, is the one who wins.
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As for an "expanded council" being "too big to function" -- please note that this is exactly how many modern nations work today, the "representative democracies." All the citizens (
millions of them!) vote for "representatives" who actually form the government. In the USA's Federal government, there's roughly 450 elected offices; the UK's Houses of Lords+Commons is over 1400 IIRC. And then there are a huge number of state/province/county/parish/etc representatives, also elected. The size, complexity, and variety are staggering.
So "growing" the active "wizarding world" membership is clearly viable.
And it's terribly, horribly necessary: there are increasing numbers of Wizard-level talents going Warlock, and needing to be killed. First off, that's horrific in its own right, as these people were mostly victims of ignorance, who
could have been decent upstanding Wizards if only given proper training; it borders on being "negligent homicide" on the part of the WC. But from a purely-cynical & self-interested perspective: the Wizards
need those warlocks they're killing. The threat-levels from the Supernatural world have increased (those Rampire punks almost took them, fer cryin' out loud!), and look to be increasing further. The Black Council is still operating without any overt WC awareness or opposition. The White Council is losing.
But it's not just the Wizard-level talents. Harry has been impressed, more than once, by sub-wizard level Wards. The Ordo Lebes had surprisingly-strong wards they collectively-raised on all their doors, and put similar wards up for Butters. The Paranet exists largely to help the lower-level talents survive under these new threat-levels, and it has largely been succeeding. Talents like Paranoid Gary & Mort, in their specific spheres,
exceed anything the WC can muster! And there are
millions of them, not mere thousands.
Those millions are
essential if the WC is to spot, educate, and organize the talents of the world into something that can survive the upcoming apocalypse.
And not as the second-class-citizens you suggest. Most of them are modern folk, and won't be willing to suffer that kind of prejudice & stigma.