The thing about culture is that the 3 early trees provide most of your
culture output for quite some time, and are often your primary source of culture. All the following trees provide little culture in comparison, and not in the amount needed to compensate for the increased culture cost for the next policy.
Also, the 3 early tree provide you
culture by following their theme: Tradition focus your capital and fills it with culture specialists, Progress rewards you for technologies and buildings (could as well reward for completing improvements), Authority rewards you for expanding and using your military might (kill, conquer, tribute, garrison).
Meanwhile, other trees provide a small generic culture bonus ("building provide +X
"), rather than rewarding actions appropriate to their theme. You don't get more culture from Piety by, for example, converting more cities or getting more followers. Nor from Statecraft from completing city-state quests and rigging elections.
The exception for low culture output is if the civ has a good source in its uniques, like Brazilwood camp.