I think the issue is that since email is more and more required to interact with the Government services, they should also provide a usable alternative. Why have your citizens rely on random foreign services from which they may be cut off because a bot somewhere is having a bad day?

In France at least, many people (mostly the elderly) are having a hard time using computers and such. Some Government agencies have dedicated personnel to help them with filling in the forms and such on dedicated computers. It could probably be easier for them if they also provided email instead of relying on a third party provider. Grandma lost her password? No biggie. If she has her ID, we can reset it for her. Good luck getting any kind of support from Google / Yahoo in such a case.

Of course, I will explicitly say that I would be very much against such a service being compulsory for the people. I just think it should exist.

Price isn't the issue, the issue is that marginalised people can be denied service outright. E.g. if you don't have a phone you can't sign up for many of those services. If you have an unusual name you may be rejected. And if you have unpopular political views you may be kicked off.

Cost aside, a solution needs to be highly available. Third party services can not guarantee your email will be available for the duration of your lifespan.

There is also the issue of data stewardship, (democratic) governments can ensure independent reviews and be held accountable for security breaches and data misuse. They could also be held liable for losses incurred by service defects.

arbitrary account shutdown is a known issue with free email. losing your gmail account without explanation and with no recourse can be an awful situation for anyone, especially for vulnerable populations. This leaves the options of forcing private orgs to maintain email addresses or have a gov email for every citizen, both of which have significant drawbacks.