I do think that our social structure would radically shift and possibly break, and it is impossible to say if what would supplant it would be better or worse. Although, at last check, creatures without emotion were definitely the dominant species. I have often wondered recently whether the evolution of emotion was a short term benefit vs. long term loss move.
I do think that we're conflating a few things with emotion that perhaps we shouldn't be. It is important for the purposes of this discussion to understand what emotion isn't:
-It is not motivation. Hunger, Thirst, Craving, etc. are not emotions.
-It is not stimulus. Pleasure & Pain aren't emotions.
-It isn't preference. Even creatures without developed nervous systems display preference.
-And it's not a necessary basis of morality.
Now if all those things went away we would become a society of apathetic, insensate, undiscriminating, serial-killers. And I think that would definitely be bad. Just removing happiness, sadness, love, etc., while certainly a horrific idea to use from our current point of view, is a harder distinction to call.