> The difference I don't get is: why is buying $1,667 of stock and paying $333 in tax different from buying $2,000 of stock that you will later realize 80% of? You spend the same total amount up front and get the same result later.
If $1,667 is a correct valuation for the stock -- meaning, the stock is valued by a liquid and well-functioning market -- then maybe there is no difference! From that perspective, there's no difference between writing a cash check for $333 and keeping the principal, vs. selling $333 of your principal and having a lower return in the long run. The long-term expected value is basically the same, you're just investing your money in a lottery ticket. But the lottery ticket is available to anyone else, and it's (in theory) fairly valued by the market.
But let's suppose that $1,667 isn't a fair value determined by a liquid and well-functioning market. Let's suppose you have strong reason to believe that this stock will be worth quite a bit of money, and moreover the market valuation is low because it's an asset that only you have access to purchase (e.g., because you're a founder with pre-IPO shares that can't be purchased for any price on any liquid market, and so the valuation is something absurdly, comically low that your lawyer scribbled on an Operating Agreement in order to minimize your taxes.) You're certainly not going to sell $333 of your massively undervalued assets to pay the taxes.
In that case the whole logic of the Roth IRA falls apart. The Roth IRA is supposed to be a savings vehicle for the middle class, where investors pay a tax on income received, then get a tax deduction on appreciation (i.e., one that is subsidized by the US tax payer.) But what is a "fair" way to calculate your income when it includes illiquid stocks? For certain assets, the "fair price" is literally whatever my lawyer says it is. So allowing highly illiquid (and not-well-priced) assets into this system seems like an invitation for abuse.
There is a separate question about whether the total Roth IRA tax benefit should be capped to something like $10m in your lifetime even when restricted to fairly valued liquid assets. After all: the US taxpayer is subsidizing this as a middle-class retirement program. But disallowing the inclusion of weird, illiquid assets might be a good idea as well.