Sort of tangential: is there a reason why Robinhood et al don’t have a “build your own index fund” tool? I’d really like to pick my own basket of stocks, then invest in them all with a “single” buy according to my weights.
If your "index fund" includes a few stocks that have large share prices (e.g. TSLA, AMZN), then to buy a single "share" of your fund would require quite a bit of capital. I don't believe the retail level investors that Robinhood targets are quite at that level.