I think I finally understand Office 365 Groups. I have been thinking of them as a competitor to Team Sites, and in that role they fall short. However, it is true that a few (or more) users may need to start working on a project together, and often the process to request and configure a team site is more than they want to deal with. Right or wrong, the solution for many people in the past has been to go around IT and just use services such as Dropbox. So thinking that Groups somehow replaces Team Sites is wrong; Groups replace the 3rd party tools that people have been using instead of Team Sites. Will Groups replace some team sites? Most likely. But the team sites they will replace are the ones where structure and process really weren’t needed anyway.
I’ve seen quite a few people asking for the ability to turn off Groups for many users. I understand the concerns that those people have. But now I think I get Microsoft’s perspective. If Groups are turned off for some users, those users will still have access to products from Microsoft’s competitors.