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.