Personally I just think your distinctions are a bit idealistic. Maybe useful as abstract definitions, but too removed from real world economics to make strong statements about it.
For example, a regulated market economy is kind of the natural state of capitalism, unless perhaps you zoom in on single transactions. As capitalism was struggling to emerge out of feudalism, the newly emerging capitalist class had to contend with governmental entities that arose out of feudal economic relations (and thus were geared towards protecting the power and wealth of the landlord class against the peasant class). In that struggle, as the capitalist class gained dominance, they tended to enact laws that protected their interests against both the old landlord class as well as the new working class.
In regards to central planning, that’s a tendency of complex economies to drift towards for a variety of reasons. Capitalism tends towards monopoly (because monopoly is the most profitable state an enterprise can strive towards), and in later stages of monopolization, the economy is de facto, if not de jure, a centrally planned economy. ln the US, a large amount of our industry and distribution is centrally planned by corporations like Amazon and Walmart, large agriculture corporations, etc. And I imagine companies are going to continue to consolidate.
The big problem is this central planning is done without our or society’s best interests in mind, their primary purpose is to benefit the company’s shareholders. What some of us theorize is that once it reaches a point of consolidation, that infrastructure can then be seized, and systems can be set up such that the efficiency and whatnot is preserved, but the purpose is changed to benefit everyone (as much as possible) instead of a small number of shareholders. That’s very theoretical and general, of course. The specifics and nuances will depend a lot on the specific conditions we live in.