They needn't have. Regardless of all the bruised feelings and harsh words, the Independent Counsel Act was there to save the day. This isn't a cost-efficiency problem. The point is to see that any probe of the president's people is done with impartiality and without fear or favor. It's the grotesque lack of proportion inherent in the law.
Everyday prosecutors wield an awesome power over suspects' lives in the best circumstances.
Using the investigatory and legal powers of the state against an individual requires restraint and judgment that the realities of limited resources and competing cases summon forth and reinforce. He has no competing cases. He has no budget to operate within. If he wants extra attorneys or investigators, they're his for the asking. It's a little like giving Captain Ahab a ship, a crew, harpoons and a highly publicized whale and then wondering why the bloke turns obsessive-compulsive.