There are huge economies of scale in finance as well. The time it would require you to maintain the index would most likely cost you more than the management fee on the index.
Your brokerage software could make this easy. E-Trade could have a feature where you can buy/sell the S&P500, Russel2000, or total US index. You put in the total amount to invest and it does the rest.
That's obviously not what the parent comment is talking about, since they're holding it in contrast to index funds. They're talking about directly holding the securities involved.
Roboadvisors do actually offer this if you have enough money. The only advantage AFAIK is being able to tax loss harvest the greater volatility from individual securities.
Fractional shares are synthetic, so you can't vote them. At that point the way to do it is to have an index fund with bylaws that it votes shares as the members want.