Those totalitarian impulses and instincts seem to be independent of central place theory. Its theory seems to be focused on logistical distribution in a “tabula rasa” (empty slate) area, for maximum efficiency at first.
http://en.wikipedia.org/wiki/Central_place_theory
I would imagine this as a formative model only, that once in place would adapt to inequality over time. Instead of urban planning, it is regional planning.
As someone noted in the US, the new major cities in the western US all look like Dallas. An urban center surrounded by suburbs, which is itself surrounded, more or less, by a freeway, that bisects the metro area at places. This is a more American model, whereas central place theory is more European.
These European models can be seen in Germany, France, England, the Netherlands, etc. That it is associated with the Nazis matters little outside of Israel.
Be rest assured that the Dallas model in America has been replaced with heavy environmental spatial planning ideas borrowed from Europe - which are anti-private property and strongly tends toward totalitarian state control - http://www.americanthinker.com/2012/01/green_lebensraum_the_nazi_roots_of_sustainable_development.html.
The Wikipedia page you point out really just focuses on what a central place was as a definition rather than an applied science relative to making planning decisions. It does not talk about how planners have used that definition to make master planned communities for us all. Christaller was given that opportunity by the Nazis to start putting his so-called principle into practice, and much of that planning revolved around what today we would call environmental sustainability under the auspices of Konrad Meyer and the SS where a synthesis between racial development (blood) and harmony with the landscape (soil)was explicitly sought. Christaller’s central place theory under Nazism started with rural farms around small villages and went from there ...
You are certainly right about regional planning. Christaller said, “The aim of regional planning … is to introduce order into impractical, outdated and arbitrary urban forms or transport networks, and this order can only be achieved on the basis of an ideal plan – which means in spatial terms a geometrical schema ... Central places will be spaced an equal distance apart, so that they form equilateral triangles. These triangles will in turn form regular hexagons, with the central place in the middle of
these hexagons assuming a greater importance.” None of this can be accomplished by letting people freely come and go ...