My point is that something like the New Deal doesn't just happen because everyone decided to get out of bed and vote one day. There's a context to understand and that context is that outside pressure and extraordinary events were necessary for it to happen.

Things didn't get better because just that many more people decided to vote and things didn't get worse because people stopped voting. The numbers just don't bear that out. We've been stuck in the band of our modern voter turnout rate since before the New Deal. So if the claim is that Democracy works when everyone votes and the example is the New Deal, then it doesn't support that claim. So if differences in voter turnout can't explain that outcome, you have to look at other factors.

As for how radical it was. Sure, capitalists didn't like it. But fundamentally it left power in the hands of those capitalists. The quote is just providing insight on how the people involved thought/talked about it. The evidence is all the history that followed that. They kept their money, their influence over the political system, and given time, they used that to dismantle even something as reformist as the New Deal.