Keeping high spending while at 100% admin_efficiency can have benefitial effects:
(1) Your bureaucrats get more money, so they can buy more goods. That means more demand on the world market (which is good if you produce many goods), less MIL for them and (iirc) they are more likely to promote to capitalists.
(2) Other pops are more likely to convert to bureaucrats, which creates a buffer for the later stage of the game. Remember that issued social reforms increase the number of bureaucrats you need for 100% efficiency.
(3) High ADM spending helps crime fighting, which prevents some annoying province modifiers from popping up.