IMO, this is like asking "is it still a democracy if the people don't decide on every bill directly?" In a sense, the answer is no–but I still feel comfortable using the word democracy.

I'm going to keep going with this analogy—IMO, idolizing the idea of a completely unregulated market is akin to idolizing the governing structure of ancient Athens. Yes, the rules we've added over the past millennia make us less free in a way—but they also make for a more sustainable system. These refinements are a sign of maturity.

I think you're caught up in an is/ought conundrum though: "idolizing the idea of a completely unregulated market" is the discourse! That's the pro-side rhetoric in a nutshell, how bills and laws get passed, and how the (US) economic system is constructed. So don't blame my inference, it's just what I'm reading in the newspaper.