Every time I see a reference to the meme that the top M% of the population has N% of the total wealth for some N > M, I always want to point out "Inequality in Equalland" (http://www.daemonology.net/blog/2011-01-10-inequality-in-equ...), a thought experiment which shows that even in a society equal to the point of parody, 20% of the population would hold at least 64% of the wealth just by saving for retirement over the course of their careers.
It makes slightly more sense to talk about income inequality, and much of the article looks at what a top-tier income looks like, but it makes little to no sense to gripe about wealth inequality.
Even beyond income, I think that what we really ought to concentrate on is inequality of consumption. If some person is immensely rich but lives modestly and either gives most of their income to charity or reinvests it I don't really see how they're meaningfully contributing to inequality. And if they just pile the money under their mattress we might as well just print money instead of taxing theirs, the net effect on everyone else is the same but the miser gets whatever emotional gratification they're seeking.
I agree with the first half of what you said; getting bothered about income seems like sour grapes, but I don't see anything wrong with finding wastefulness tacky. (With the caveat that "wastefulness" remains subjective.)
However, I disagree with your claim of "just print money"; doing so devalues currency for everyone, including people genuinely saving money for the future.
If we wanted to maximize the value of our money, we could straightforwardly start reducing the number of dollars and introduce widespread deflation. What we do instead is try keep inflation predictable, so that interest rates on savings and debts can easily factor in inflation and neither savers nor borrowers are treated unfairly.
Getting back to the case in question, the link between printing money and inflation isn't magical, the mechanism that turns more money into inflation is people using that money to bid up the prices of goods and services. But the money that was in the mattress wasn't being spent on anything. So both taxing that money away and printing new money result in exactly the same amount of new money chasing goods and services.
You don't have to take my word for it. During '09 the supply of dollars increased by a pretty sizable amount, but we actually managed to have negative inflation because the Fed's interest on reserves policies managed to keep all that new money in the vaults of large banks rather than in circulation.
It makes slightly more sense to talk about income inequality, and much of the article looks at what a top-tier income looks like, but it makes little to no sense to gripe about wealth inequality.