This raises some of the BYOT (as opposed to BYOD) discussion from the past.
Are you better off having your teacher, use the tool they are most comfortable and familiar with, or the tool the school is providing?
All sorts of reasons why one might win out over the other.
That said, my hope is the Google Classroom will eventually allow for website/blog features, so that the teacher can do all that from one screen.
We have one teacher who has had a current and updated webpage for at least the past decade, going from Standards Into Action, to Teacher's Workplace (?) to two different iterations (soon to be the third) of a page on our school website (Site@School, Joomla, Wordpress)