Why does Triforce get 20% CDR while Lichbane only gets 10%?

I get that lichbane does more damage, but that damage is only until mid - late game when you have more than 300 AP. At all stages before that, triforce does about the same amount of damage as its scales on the champ lvl, not their AD.

I get that it cost more gold, but it also gives a lot of stats that make the item function well on its own, while Lichbane depends on more CDR and AP from other items. Triforce has enough attack/move speed to function well with none AD items.

Overall triforce is a well rounded AD item that works well on its own and doesn't really depend on other items. It is probably the most gold efficient item in the game.

I'm not asking for Lichbane to get a ton of other stats, just 20% CDR so I have a better chance of procing the spell blade passive with low cooldown abilites.

I don't mind a gold increase on the item. It may even be added as a the new "Haste" unique passive that give an additional 10% CDR as long as you only have one item with "haste"

What are your thoughts on Lichbane vs Triforce?