I tend to agree, Tradition gets you more happiness/citizen, more gold/citizen, and overall, more growth, but Liberty gets you a faster CB rush.
You get 4 cities out faster, and you impede growth in the capital less while doing so. Liberty saves a ton of turns prior to t60, whereas Tradition really gives most of its benefit over the course of the game. Also, the free monuments save turns mostly in the expos, but the settler bonuses help a lot in the capital, which is your main early production center.
Collective Rule gives 50% faster settlers + 1 free settler. This works out to a significant early advantage. A settler costs 115(?) hammers to build in a normal ancient era game. +50% production = -33% time, so if it normally would take you 9 turns to build a settler, it takes 6 with Liberty. If you build 3 settlers, what would normally take you 27 turns only takes 12 because of the free settler. It's actually more like 10-11 because of the +1 production/city. Furthermore, the food bonus to settler production tapers off, so the extra food in the capital doesn't contribute as many hammers to settler construction. (Extra hammers come at +1/+2/+4/+8/+12 food, so the best return on investment is at +2 food)
16 extra turns of stagnation in your capital is a difference of as much as 2 population, which, in the early game, compensates for the growth advantage of Tradition. 16 turns of lost production is not trivial either. You can typically build at least 2 archers with that.
You will typically have time to build at least one archer in your expos before you CB rush. That's another advantage to getting your first settler out on t30 instead of t40, but it's canceled out by the need to build a monument.. sort of.
Regarding monuments:
Republic gives + 1 production in cities, and 5% while building buildings. A monument is 40 production. A typical expo starts at 3 hammers, if you plant on hills, so that goes to 4. Reducing the cost of the monument (effectively) from 13 turns to 10 turns, for a savings of 25%. The +5% to buildings gives a net savings of 30% on that monument. x3 = ~1 free monument.
Tradition saves you 160 hammers on monuments, only 40 of which is in the capital. Including the free worker, which is 70 hammers, Liberty saves you about 400 hammers in the early game, most of which is in the capital.
Add in the tile improvement rate, and the end result is: Faster CB rush. And the synergy with Pyramids is game-breaking if you get it.