There's only one pie. If it gets bigger, it gets bigger.
The money isn't in a mattress under the bed. Some of it is in real assets like property and paintings, to be sure--but the assets are "getting bigger" and once money's put in they don't take any more money. Suddenly you "have" $1 million in assets where you paid only $500k, but you didn't pay additional money and the money pie isn't any bigger. At the same time, the money that is chucked into banks doesn't just sit there. Under the reforms from the early 2010s more *has* to just sit, nonetheless most of it gets turned around and put back into the economy. It's why we have loans. In fact, not only is the money put back in, with its own multiplier, but there's a kind of bank multiplier effect that increases the money supply.
The matter with asset appreciation is a vexed one for a lot of people. My parents had a house. They bought it for $160k. A decade later comparable houses were going for $260k. Then 2009 hit and the house was back to $160k. My mother wanted to know who stole her money--she was convinced somebody got $100k. Same with the AIG stock she had in her smallish portfolio. It virtually zeroed out, and it was nearly impossible to convince her that "her money" had gone to the person she'd bought the stock from months or years before, and that nobody sucked the money out of her stock value in a way that could be banked. (Didn't talk about short sales, but that's the same thing made more complicated).
On another point, the subject line for the OP is wrong. It talks income, but the OP talks wealth. They're far from the same thing, which is why the asset appreciation bit, which is the majority of the discussion, can be tucked in. But talking about how asset appreciation favors those with more assets seems like a silly, non-outrage kind of thing, and leads to asset depreciation (stock market crashes) disfavoring those with more assets.
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