-Height Matters-

In a average 24 gram coffee brew with a standard 60 degree cone shape, the dry brew column is 2.25 inches tall. In a average 24 gram coffee brew with a 70 degree cone shape, the dry brew column is 3 inches tall. The 70 degree brew column is 33 percent taller causing the brew water to travel further through the brew column. Therefore, by increasing the height of the brew column you are increasing the water to coffee contact.  All else constant, increasing the water to coffee contact results in more extraction of coffee solubles. 

Secondly, the brew column serves as a filter. As the water moves through it, coffee matter are carried downward. Most of the non soluble matter are eventually trapped within the column, therefore acting as the primary filtering mechanism for the brew. The taller the brew column, the more non soluble coffee matter will stay in the brew column,  resulting in higher cup clarity.

In short, a taller brew column can help achieve higher extraction yields of coffee solubles and enhance cup clarity.