2) You have an exception to such laws for exigent circumstances or implied consent.

Here is the flaw in your argument: We don't have to nail everything down to nail part of something down. We don't have to define "exigent circumstances" mathematically or put the badge number of authorized fire marshals in the statute. That doesn't mean we can't do better than obscenely broad and vague nonsense like "unauthorized access to a computer."

There is a reason we have laws more specific than "anyone who does anything bad shall be punished by a fine of up to one hundred trillion dollars or up to one thousand years in prison."