This seems to have started with EA from way back. Take for example Mirror's Edge, it's purely singleplayer but it has leaderboards and time attack modes. I gues sthe primary fear from gamers is now we'll have singleplayer games with tacked-on multiplayer just because it's a requirement.
One good example of that is Spec Ops: The Line, even the developers, Yager, hated the idea and they declined to do it, so 2K hired a different studio, Darkside Game Studio (ironic name), to make a generic multiplayer mode that nobody is playing.
I feel that resources should go into funding a complete and satisfying singleplayer experience rather than risk cutting anything from it for a subpar multipayer feature.
If "achievements" count as an "online feature" then I'm not worried about EA's decision. Devs can easily slap those on to any singleplayer experience.