Companions have individual reactions to relevant MSQ segments and quests so by definition anyone you don't have is someone whose reactions you can't (potentially) see. Most of the time it's not essential but there are situations like the second segment of Winter Wolf where your party composition can affect the outcome of the quest, and having certain people in the third part of the quest makes one of the fights easier by preventing you from starting it with a party-wide debuff, to pick an example.
For more substantial things, you're required to bring Tui to part of the quest in order to complete Shadows Over the Sun; you don't need to bring her for the conclusion of the quest (just the setup for it) but you really should. Also you'll obviously be unable to access her upcoming quest, or the one Garde has teased as a plan for after that without her, so that's content you'll be missing by definition. For another missing companion example, not having Azzy potentially soft-locks you out of finishing an Act 2 quest.
