The biggest potential cost of someone in the US, with employer-tied healthcare, seems like medical. You could hit the unlucky jackpot and have a seven-figure+ medical bill over the course of a few years or life. So let's set "able to handle that for yourself and your family" as the baseline for being considered independent, since that's probably bigger risk than, say, "owning but then losing a multimillion-dollar-home to a flood" or somesuch.
But I also don't think this term is generally understood as poorly as you suggest.
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Responding to context complaints aside, you're still talking income tax, not wealth tax. My question was what this hypothetical negative-use wealth tax looks like, since the further-upthread post had suggested taxing wealth instead of using income as one of (several) proxies.
But also, my hours have not increased with my compensation in the manner you suggest. I know that every additional dollar loses 40% or whatever of it, I still would rather have it than not have it. 5%, probably wouldn't care, but would I still want more autonomy and responsibility at work for the sake of more feeling in control? Maybe. Maybe not. There are both financial and non-financial sides there, but if income was the sole basis for choosing our roles, we'd be in a very different-looking world.
So that's why I'm skeptical that a wealth tax would make me give up having big dreams—the personal safety net and toys are still incredibly appealing.