Consider the logical extreme: infinite wealth
So, at some point, wealth becomes enough to turn everyone into a spellcaster. At some point, using items is better than anything you can do with a feat or class feature, even spellcasting. If anything, non-spellcasting features become more important, because spells can be replicated with items and other class features often can’t.
But no one, so far as I know, has really tested where that point is. I’ve heard of campaigns where there’s been actually-unlimited wealth, and that’s how things tend to go. How much finite wealth you need for that to happen, though, I don’t know—and don’t care to figure out.
About smaller increases to WBL
Doubling WBL will certainly not be enough to turn everyone into a spellcaster-via-items. At lower levels of hyper-WBL, the effect on tiers will be very difficult to predict.
Certainly, generally speaking, mundane characters “need” magic items where spellcasters merely “want” magic items, so mundane characters could arguably be better off, but things are going to depend an awful lot on the precise number of levels in the precise classes in question, and the items available. For example, imagine quadrupling WBL—it allows a paladin to get a +2 enhancement to all four ability scores she needs when otherwise she’d only be able to afford one—quadrupling her enhancement. By the same token, though, the wizard can now afford a headband of intelligence +4 instead of +2—same four-fold increase in gold-piece value. And while the paladin definitely needed all that enhancement, the only thing the wizard needed was Intelligence—and he got it. Who has benefited more? The wizard is certainly still more powerful than the paladin, that much is sure.
Lack of data
As I said, where you find yourself with “enough wealth” such that you might as well have “infinite wealth” is unknown, and likewise, the exact effects of finite-but-more-than-normal wealth is extremely difficult to predict. These things are not coincidental—they both stem from the simple fact that we don’t have a lot of data available on hyper-WBL campaigns.
There simply don’t seem to be a whole lot of such campaigns out there in the first place—and most seem to be “I’ve accidentally given out overpowered items, how do I get my campaign back to normal?” This question discusses a high-wealth game, rather than some specific problematic items, and it’s about the only one I know of for that.
I suspect that the reason why people haven’t really done such campaigns, either accidentally or intentionally, is simply because accounting for gold pieces really sucks. I’ve had characters or whole campaigns that fell well behind on items simply because nobody wanted to figure out wealth. Optimizing your use of wealth is an extremely, extremely difficult problem, and even just a casual decent approximation of optimal use takes far more than casual effort. It’s not even necessarily easy just figure out what your wealth is, when you consider the possibility of selling off portions of what you have but for less than what it’s maybe “worth,” but maybe you can get more value to you that way, and so on.
These problems all get easier the less wealth you have. Since the DM needs to think about your items in the context of determining appropriate encounters, having less wealth can also seem to make their job easier as well (and actually does if they don’t care very much about intra-party balance and having all PCs contribute roughly evenly).
So since people aren’t playing such campaigns, or at least, aren’t discussing them ad nauseam online, as people do with hypo-WBL campaigns, we really don’t know—can’t know—what the effects are going to be. It’s vastly too complicated a system to predict deductively—empirical evidence is mandatory, and we just don’t have it.