That’s… called neoconservatism (and weirdly neoliberalism is a basically a synonym). Classical liberalism is closer to libertarianism, is usually against government involvement in private matters. Those ideas are much older and came before McDonalds, Goldman Sachs, Cayman Islands, quantitative easing, and trillion dollar bailouts type of economic system of today. Sure, Reagan and current day republicans steal rhetoric from classical liberalism all the time, but the political-economic system is unrecognizable.

The “big corporation-style” capitalism is definitely a new flavor, and unfortunately that’s seen as centrism today, adopted by moderates of all political sides across the western world and even beyond.