I agree with the premise, and yet also disagreee.
G33k raises a few good points - namely that the White Council is simply a product of it's time. They aren't all that adaptable. They do have huge resources, but they also are heavily hamstrung by their own internal political problems. They only appear on the outside to work together; internally I would say it's far less organised. Think the UN, but at a smaller scale (the whole White Council is barely a few thousand wizards, given that their wardens only numbered about 200 in Dead Beat).
I agree that Jim probably would find it hard to emulate an Illuminati-esque organisation given his presumed lack of exposure to one. I also agree that the rich and powerful tend to have armies of servants to support them. I suspect the really powerful wizards probably do have large networks of allies and servants - we just haven't seen that much of this yet. But each of the Senior Council has shown glimpses into their networks. The Merlin, of course, has an entire organisation under him to direct. But the Gatekeeper has shown his relationships with the Faeries, Listens-to-Wind has shown his relationships to the Forest People as well as other local magical groups, Martha Liberty has connections amongst the Loa, La Fortier had deep relationships with a lot of European and other factions (which Cristos has taken over), Simon had relationships with the vampires it seems (as well as other European connections), and of course Ebenezar has been shown with the most connections (Vadderung, the Grey Council, Kenku, etc). Part of what makes the senior wizards so strong is their allies and political strength, on top of their magical might and skills. Jim has also said they each have their own demesnes to retreat to...which gets interesting.
We just haven't seen everyone put their cards on the table, as it's a Harry-centric story. Remember, the White Council had many allies to support it during it's war with the vampires. And when it came time to finish them off, there is a decent theory that Harry's involvement with destroying the Red Court and ending the war was somewhat planned (potentially that Harry acting unbeknownst to himself as a sort-of black ops agent). When the temperature ramps up I wouldn't be surprised to see people start to put their cards on the table.
I also believe that the White Council is very strict about allowing outsiders in - as G33k points out it is a security issue as much as anything. But they also seem to big on the idea of not involving vanilla mortals in their affairs. So the hiring of clued-in mortals seems a bit tricky.
I suspect the reason they have survived so long is partially to do with the appearance of power. They have overcome much in their history, which gives the predators pause. And Ebenezar has hinted that the White Council has nearly been wiped out several times over. So yes, they probably have more than a few supernatural benefactors invested in their survival. There is a reasonable theory that Vadderung (among others) caused the creation of the White Council - which makes sense given that he personally trained the original Merlin. So he and those like him would be invested in it's survival. I would be willing to bet he puts out a lot of unseen fires. Let alone beings like Uriel.
Not to mention, at the end of the day it's a group of several thousand of the strongest mortal magic users on the planet (with the exception of certain dark wizards and so on). That power combined, that knowledge combined, makes them a match for many groups. Yes, they are still minnows. They are nowhere near the top of the food chain. But they can probably hurt just about any being, and that alone is scary. Mortal magic after all has special and unique properties that the other supernatural beings don't have. And the White Council is probably the largest well of mortal magic on the planet.
I think the White Council's greatest threat ultimately is itself - and that is certain to be its downfall. Nothing lasts forever and the White Council is assuredly at the end of its time.
Sorry, only just read Snark Knight who sums it up more succinctly and clearly than myself. Agreed.
The WC suffers from organizational inertia. Almost every large organization has this issue, irl think cops, UN, military and others. Every one knows the organization needs to changeonly noone agrees on what that change should be.
This is why i think the war will benefit the WC IN THE end. New recruits to the Wardens Carlos and such picked up stuff from the old guys and from Harry. Harry mentions that most new Wardens try to model Carlos.
Harry for all his talk is anti social and only attends meetings which are bad news for the council. He does not network. Carlos does.
The WC is believed to be tough. Everyone thought that the war wasn't going to last with the WC winning that it didn't, is a sign of the powers that supported the RC. The WC needs to change to survive but calling it weak is a bridge to far