Email is a neutral protocol, in a natural monopoly, very hard to replace unless you want to choose a state sanctioned monopoly like you would to Facebook's Whatsapp or Apple's messenger.
This sounds like fatalistic throwing the baby with the bath water, I know that there's a fine line between operator's error and bad system design, but when a piece of technology has been stable for 40 years, and there is a fuck up, you can't reaally blame it on the tech.
If there's really sensitive info like informants or HIV patients, maybe implement some serious access controls so that not even operators have access to that sensitive info.