The problem isn't that people don't pay taxes on unrealized gains, the problem is that people pay low taxes on realized gains, and usually no taxes on the very large gifts and estates. A tax on unrealized gains of billionaires raises a little bit of money without dealing with the giant structural unfairness in the tax system—which, really, is why it might be politically viable.
Actual tax fairness would be simple and not require a tax on anyone's unrealized gains: special taxes (with low rates and broad exemptions) on long-term capital gains and estates and the givers of gifts would be eliminate, and all of those things would be regular income to the recipient. Windfall gains and gains requiring long-term effort/ownership would be addresaed by allowing everyone the option of advance tax recognition of future income and deferring windfall gains over a period of years, both tools to smooth income.