The identification of "freedom of market participants to do whatever they want" as being the "free" in "free markets" is exactly the problem here, in my view—and I'd go further and claim that confusing the two things has been a deliberate sophistic practice (among others, chief among them being "please don't notice I snuck in a couple sketchy axioms and 'as we all know's at the beginning, so that you accept the hundred pages of 'reasoning' based on them that follow") promoted by figures in some allegedly-intellectual circles, to make themselves useful to those who find that kind of thing beneficial, and so to personally gain from being professional BS peddlers.
(I'm not correcting you, here, just adding on—I'd guess we basically agree on at least the first, and most directly relevant to your post, sentence of the above)
Sometimes it is. Sometimes it's about making sure you can be competitive, and you as a particular business don't have an inherent right to be competitive. Instead it's a collective right to have access to competition.
A right to participate in a reasonable way does not go far enough in many markets.
I'm only learning about the history of economics myself. It seems a lot of people interpret Adam Smith as advocating against any government intervention, even in the case of price-fixing. For example: https://www.adamsmith.org/blog/regulation-industry/misreadin...
I'm not convinced that it's deliberate. You can draw a parallel with free speech: is it about letting anyone say whatever they want, however loudly, as much as they want? Or is it about ensuring that everyone has a voice, i.e. preventing the loud people from drowning out or otherwise intimidating the quiet ones. You could well argue for the latter, but many people in the West assume it means the former.