Pretty sure the most essential class for damage output from an optimized standpoint is the monk. There are 3 feats which give massive damage increases- Great Weapon Master (-5 to hit, +10 damage), Sharpshooter (same), and Tavern Brawler (+6 to hit, +6 damage). It should be obvious which one is the best mathematically, of course. I’ve seen many builds which deal 50+ damage per hit and / or have 6+ attacks per turn, all of them involved monk, most involved Barbarian, some involved Rogue or Druid, some involved Warlock or Paladin, and at most they involved 2 levels of Fighter for action surge. Haven’t seen a build with 11 levels of fighter which comes close to the damage output of those builds.
But it is funny to me to say that Fighter is the most essential class for damage output while talking about the benefits of haste! Haste, Hold Person, and so forth are *far* more impactful than what flavor of Martial you’ve got kicking around. Command to drop their weapon, or a Rogue stealing them before the fight begins, will do far more for the fight than having a 3rd attack. When we’re talking about impact, all classes can dish out damage. It’s a matter of what else you can do; for Fighters that comes entirely from their subclass for Eldritch Knight or Battlemaster, and doesn’t come at all for Champion.
