Can you explain this statement please? I thought taking an extra 3 culture per turn would make you gain policies faster, not slower. Is it just that you are one policy behind?
The idea is that your policies in other trees cost more culture. So for eample if you wanted mediocracy, it would cost 240(?) culture, instead of 135 culture if you took tradition first (again on Epic speed)
However, I think its offset by gaining more culture with tradition and therefore gain more SPs (in general) in the same amount of time.
so lets assume goal is mediocracy, on Epic, no huts, and build a momunet first.
first SP costs 35 culture - get at approx turn 20
Next SP costs 65 culture:
with Traditon (6 culture per turn) - 11 turns (turn 31) - get liberty
with liberty (4 culture per turn) - 16 turns (turn 36) - get free worker
Next SP costs 135:
With tradtion (7 culture per turn) - 19 turns ( turn 50) - get free worker
with liberty (4 culture per turn) - 34 turns (turn 70) - get mediocracy
Next SP costs 240(?):
With tradition (7 culture per turn) - 34 turns (turn 84) - get mediocracy
With liberty (4 culture per turn) - 60 turns (turn 130) - get (whatever)
... ok so now that I started typing this out I can't remember the rest of the SP costs.
BUT I think you "catch up" by the next SP and even if your goal is medicocracy, you get it only 14 turns later (which don't get me wrong can be important), and you also will have a much larger area and more tiles to choose from... and therefore (potentially) more hammers, food and/or gold. (and ofcourse this all changes if you build more cities, a wonder, somehow get philosophy early and build a temple, don't build a temple etc).
The only way I wouldn't take Tradition first in any game, is if for some reason I was not going to take the tradition tree at all... and given the nice SP in it, it would have to be a very specific and situational strategy.