No. It isn’t enough that they know their name or can physically sign their name. “Incapacity” refers to an inability to receive and evaluate information in order to make reasoned decisions. Also, estate planning documents aren’t valid if signed by someone who doesn’t understand them.
Why do I need power of attorney if I’m already on my parent’s bank account?
That only lets you access the assets in that bank account. If your parent has any financial or legal affairs outside that bank account, then you’re sunk. Without a power of attorney, you have no legal authority to handle anything on their behalf outside of that one bank account.