There is some story content you'll miss if you only do one. In Shadowbringers you have to do all four role quests to unlock a bit of lore/story, but it isn't much.

Gameplay wise, there's no penalty to playing just one job. There used to be requirements to level other classes to an extent to get certain cross class skills, or to unlock your class > job upgrade quest, but these are thankfully a thing of the past. You can play the whole game with just one class/job and be just fine.