Pointing those points into an Extra Spell Action would only reduce the potential power and effectiveness of each spell.
Why? If 6 CP are spent, wouldn't they have the full MRV of their Arcanum tree for each spell?
Those points could be applied to a primary magical ADC to increase overall effectiveness. Assuming 12 CPs total, an arcanist would be choosing between something like D8 > D6 > D4 or
D4 > D4 > D4 (thus Extra Spell Action also at 3D4 max). Also, if the arcanist didn't master something in the ability tree, then spending 6 points in the Extra Spell Action would also be pointless.
If it works the same as Extra Attack, then 2 CPs grants access to the basic rank only (arcanum basic). With another 2 CPs, the character could choose any one of the magical specializations to add an Extra Spell Action, assuming the spell is known (or follows the 'read from scroll' rules).