In the 1920s, the depression hit. Things were pretty bad, so the government started taking an active role in trying to fix it. They did this by starting public works and more government jobs, each of which required money. 100 years ago, the US government didn't have much stake in what the rest of the world did. The two world wars, and the cold war put a firm end to that.
In other words, that tax money went to accomplish things. Interstate highways, electrical projects, welfare, medicare, medicaid, social security, and a whole lot of public universities are just the things I can think of off the top of my head that these new taxes paid for. And if you want to talk about government subsidies for struggling farmers and other industries, that's a whole new barrel of fish. Few of these programs were even conceived of 100 years ago, yet alone paid for.
Ultimately, without those taxes, big projects would never get done. Can you imagine the dozens of universities, millions of miles of road, or the myriad power plants that never would have been created without these new taxes? I doubt whether private citizens could or would have paid for any of this with the money they saved from not paying these new taxes. Considering that many of these programs helped the US recover from the depression and grow economically, I doubt whether there would have been enough money in existance for these projects.
Of course, that's just my opinion on why taxes are necessary for government to actively serve the public. The opposite view would be to not tax at all, have a tiny government, and have everyone look after themselves. That approach has it's own set of pros and cons that are too deep to delve into here.