Keep in mind that an "index fund" or "mutual fund" is not a legal structure for tax purposes. In the US, most mutual funds appear to be "regulated investment companies" as defined in 26 USC § 851.
The default rule is that regulated investment companies are taxed the same as corporations, paying corporate income tax on any taxable income.
However, pursuant to 26 USC § 852, a "regulated investment company" can avoid the application of the normal corporate tax regime and instead be taxed under an alternative regime if the dividends it pays to shareholders exceed 90% of the regulated investment company's income for the year, and if it also satisfies some other conditions.
Under the alternative regime, regulated investment companies are only taxed on retained earnings and certain capital gains, as opposed to all taxable income.
A regulated investment company that retains all dividends would not qualify for the alternative tax regime and so would have to pay normal corporate tax on all its earnings, subject to the usual corporate deductions and exclusions including the deduction for dividends received described in 26 USC § 243. The computation of the corporate tax that would apply is itself complicated, and it may not be accurate to say it's always worse than the alternative regime. I have not calculated any examples to see if there are any edge cases where the corporate taxation regime could actually be better for shareholders, but they may exist.
