The Wikipedia article says that when the percentage of revenue from each bracket is compared with the wealth distribution rate, it lines up very closely.

See below - one could argue that the bottom 50% numbers are extremely divergent, which is very significant, affecting half of the population (though almost none of the wealth).

Lining the two curves up in such a way would seem, to me, a reasonable approach to taxation.

It all depends what you mean by "reasonable." The numbers given by Wikipedia are here:

Top 1%: 36.9% of tax, 32.7% of wealth
Top 5%: 57.1% of tax, 57.2% of wealth
Top 10%: 68% of tax, 69.8% of wealth
Bottom 50%: 3.3% of tax, 2.8% of wealth

(with the note that this "top/bottom X%" thing is a truly awful way to present this type of data, something I would rectify if I had time, but knowing these data sets, it's probably presented in an even worse format in the reference, so...)

One argument would be that these are all pretty close, so everything's just right. Except for the super-rich, everything is within 1%.

Another argument: this is an extremely progressive tax system, because it's measured against wealth, not income, so in effect, those that have done the "right thing" and put money away are being effectively punished for it, paying far higher taxes per unit of income than their more wasteful peers that haven't been saving.

And another: the .5% out of 3.3% overpay at the bottom 50% of the curve is massive, proportionally speaking, and really amounts to the bottom 50% paying about 20% more than their "fair share" of taxes. Worse, these people make up the bulk of the population, are actually hurt by this overpayment, and the amount of money it brings in to the government is fairly negligible.

Taking things further, we could try to work out how much each of these taxes actually "hurts" people in each bracket, i.e. how much utility it deprives them of. For instance, taking 10% of a billionaire's wealth away from him clearly "hurts" him less than taking 10% of someone with a $20k/year job; typically people assume some sort of logarithmic money -> utility mapping. Under any such mapping, even a slight one (and I think most people would accept a significant money -> utility discrepancy) the current curve (wealth vs. taxes) becomes regressively skewed.

The other thing to consider is that "fair" has other meanings when you're living in a democracy, as well - at least indirectly, we should expect "occupancy rates" at each tax bracket to determine the rates that they pay. By this logic, the people near the hump of the income distribution should be best off, and people making the most should be worst off (people in the middle would not choose to shift too much of the tax burden down to the lower classes because there's just not too much burden that it can absorb, with the lowest 50% of the population in control of only a couple percent of the total wealth).

I've done some modeling of democratic influence on tax rates, and one of the main conclusions I came to was that under what we figured were fairly reasonable assumptions (and there are a lot of them), a self-interested body of people democratically figuring out tax rates will generally come up with a very progressive system (more progressive than ours under most assumptions). In order to come up with a system closer to ours, you need to make the "fairness factor" weightings very high (i.e. assume that even the poor are highly offended by disparities in tax rates), or assume that the number of "votes" a person gets has some dependence on their wealth, or some combination of the two. In reality, it's probably a combination of the two (many people feel, for better or worse, that a flat tax is "fair", and those at the higher end of the wealth curve have increased influence than their numbers would suggest) that lets our tax rates stay at the current distributions.

Anyhow, I'm not trying to suggest anything in particular from this (I'd probably tend to agree that the current system is at least within spitting distance of a reasonable compromise, obviously with some edge cases and loopholes that could be improved upon), other than that there are pretty reasonable arguments that pretty much any tax rate curve is fair or unfair, including some very extreme ones.