Even if it was for a "good cause". Let's for a moment even assume that the NSA is an all-holy entity that could never do anything wrong and that we trusted them implicitly, not because our software forces us to but because we genuinely wanted to.
Note the subjunctive.
Even then the security software would be a security hazard. Simply and plainly because there is (at least) one way to access data that is absolutely beyond your control. You cannot even audit the security level of the entity holding the additional key to your data.
If you need to give your non-tech boss a way to understand the severity, that's like having a general key to your office and the safe with all the highly classified and mission critical papers deposited at your local police force. While by itself not a problem (provided you trust your police), they are not required to give you any information concerning the key's storage or whereabouts. You will not be notified how they themselves will keep that key safe, nor do you get any kind of information should that key get stolen. You will not be notified if some potential attacker or burglar, or even a competitor, gets access to that key, legally or illegally.