Absolutely would not be a good candidate for a gov service in the US. Imagine the politicization currently applied to the Postal Service, but on the scale of everyone's email?
This argument could easily be extended to private businesses. The government has the capability of putting pressure on private entities to compel them to treat email in certain ways. The rule of law prevents such things, and I don't really want to start a thread about how the current administration has no regard for the rule of law.
Furthermore, not everywhere is the US. Why hasn't Germany done this? Or Australia? Or Singapore?