There isn't enough money in the world to insure the bank deposits of every business. Think about how big insurers would have to be if they needed to insure all the deposits of every business. "Every business should have private deposit insurance" isn't the goal of regulators because it's not a workable solution.

So instead the government acts as a sort of "insurer of last resort" by promising they will do everything they can to protect depositors in the case of banking instability.