Then why do people say "invest in the stock market for the long run by buying an index fund?"
Because the American economy has historically grown. Buying an index of Austrian stocks on the eve of WWI would have been about as effective as buying cryptocurrencies.
If you buy 100 stocks and 10 of them go to 0 you are out 10%. However, if the other 90 stocks are up more than 15% then you have gained a little money.
But, if you buy 100 different stocks by hand then you pay 100 different transaction fees and have to keep track of them independently for tax etc.
There are tax advantages, but it's more complex than simply not paying short term capital gains on dividends.
Index funds require no special knowledge to build...just buy the S&P100 stocks in equal amounts and boom, so the fees for such a fund can be super low.