I don't really know if there is any connection. I'm just saying if Mars was colder in the past then some remains of these spider like formation might be found at lower latitudes. Personally I don't think there are many similarities either, but it would be important if such remains did exist. The question then might be if these never existed at lower latitudes, why not? Perhaps a reason is around the polar areas the temperature is more constant around summer because the sun doesn't set. Whatever process then forms these branches, terraces, etc might need a fairly constant climate to form them.
Once you get outside the polar area temperatures whether they are for liquid CO2 or water only last for a short time so it would seem a model would have to include rapid heating or cooling for what we see. Your own theory seems to need this heating for example but would behave differently if the air was cold enough so the CO2 didn't sublimate quickly. Imagine if around the south pole there was a point where liquid CO2 sublimated very slowly at that air pressure at a given time of the year then one would see features made from that. It seems the temperatures at some places around the south pole reach zero or close to it, so possibly features would be formed there by liquid water.