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 I don’t think I necessarily disagree with what you said, but that seems a bit like a goal post shift. That’s not actually an argument in favor of taxing unrealized capital gains. If I may put forth arguments against: 

1) The new proposal is framed as a tax on the ultrarich. The same was true of the new income tax in 1913. If given the power to tax unrealized gains, expect the feds to expand the tax to ordinary people. If not directly, then indirectly as inflation makes us all billionaires on a long enough time horizon and the income limits are not inflation adjusted.

2) taxing unrealized capital gains becomes infeasible when trying to assess the value of more illiquid assets, like paintings and other collectibles.

3) if there is a tax on unrealized gains, will there be a tax write off for unrealized losses? 

4) paying taxes for unrealized capital gains requires either a) the immediate selling of liquid assets to pay the tax, or b) using already available cash reserves to pay the tax. This has the net effect of reducing available capital, reducing productivity, and making everyone worse off.

5) see point #2. The complication of taxing unrealized capital gains will make billionaires hire tax lawyers to fight the IRS to define what counts and doesn’t count as an unrealized gain. This is a net drag on the system, adds friction, and increases the operating cost of both the irs and the private individual / entity.

6) we already know increasing taxes in general creates the rich to flee to offshore accounts. I would expect the assets to magically be moved or brokered to jurisdictions outside of the reach of the unrealized gains tax laws. This has the net effect of draining society of assets.