Back when I was fantasizing about what I'd do if I won the lottery, I looked into family offices a bit and concluded that there's basically no point as far as the investing advice goes. It's still likely a good idea for some of the ultra-wealthy for estate, tax, and philanthropic purposes, but on the investment side? The standard passive indexing approach used by middle class individuals scales in a cost-effective ma…
There is one point you haven't considered: Even though a pure indexing strategy is appropriate, it is not appropriate to use Vanguard for this. At the billion-dollar level, assuming that the index funds had an expense ratio of .05% (among the lowest out there) you would be paying annually: 1,000,000,000*.0005 = $500,000 For that level of expense, you could instead have a one-man office or other service provider that…
Honestly a much stronger argument is tax efficiency. If you're buying the individual stocks, then even when the index is flat you'll have some capital gains and losses. You can use both these to improve your tax efficiency - the losses can be harvested to offset realized gains elsewhere, while any appreciated shares can be donated to charity and repurchased with new money, effectively increasing your tax basis.
Still, you're likely better off just hiring people to do the tax planning, estate planning, and philanthropic services. It's essentially setting up a single family office with no control over your investments.