Many use free Google, Yahoo, Microsoft email accounts; I would trust them about the same as a government provided service. Microsoft especially has a proven track record of garbage security posture.

Importantly, we need to be mindful of the lowest common denominator citizen who might have nothing but still be entitled to government services. Governments exist to service their constituents. The USPS is required to serve every US address (including mail delivery by mule into the Grand Canyon) [1], it is straightforward to provide ~1GB of email to everyone who needs it.

[1] https://about.usps.com/who/profile/