For just under $275, just about anyone can buy a share of SPY and make/lose money based on trends across a diverse array of the largest companies in the world. Without indices, you'd have to spend tens or hundreds of thousands of dollars for this kind of diversification.
It's also useful for tracking trends within specific sectors. Think tech is undervalued? Invest in a NASDAQ ETF like QQQ or NDX. Maybe you read that OPEC is planning to increase oil production and you think that's going to devalue existing oil supplies, so you take a short position on XLE (an energy index ETF).
The relative simplicity of indices means there's a lot of volume and liquidity. It's not easy to find a buyer for shares in an obscure oil company, but lots of investors would be happy to buy your energy index ETF shares.
I love indices. I'd be hesitant to invest in sectors I don't know much about, like construction materials. They're heavily affected by the price of raw materials, and lately all this tariff talk has caused a lot of volatility in those prices. Which individual companies should I get involved with? It's hard to say without a fair bit of research because it's a specialized field. With an index ETF, I can quickly take a long or short position to get a little exposure to the sector without having to dig too deep.