So they each do 33 damage as a standard. Then the fighter action surges and does 66(+25) for 91. The paladin recklessly burns 3 3rd level slots for +54 total 87. I agree the fighter using all their abilities in one round does beat the paladin, by 4
Next round the fighter does 33 the paladin burns 3x2nd doing +38.5 : paladin wins by 38
And the paladin doesn't care if the fighters got an extra 11 hit points. He can cure 55hp vs self cure 16.
But also note the paladin has +3 to all saves, maybe takes half damage from spells and can't be frightened. So maybe a fighter can nearly match the paladin in combat. The paladin has a whole bucket of other fruit compared to the fighters reroll 1 save. He far surpasses the fighter in other ways - that is the issue.
I made a math error actually, it is 36 DPR for the Paladin vs 39 for the fighter (average) with no other abilities. Round 1 going all out with all hits action surge and a hit on a bonus attack and using all his battlemaster dice the fighter does 11d10+1d4+35=98. The Paladin going all out does 2d10+1d4+15d8+9=90. But that uses all three of the Paladin's 3rd level slots, which he doesn't get back until a long rest. Every round hereafter he will do less and less damage. Round 2 it is 76.5. round 3 it is 63, round 4 it is 45. So through 4 rounds he has done 274.5 vs 215 for the fighter, or about 15 more per round if he goes all out. For the rest of the day until a long rest he will lose ground, where the fighter will consistently do more damage per round and can go Nova again after every short rest. Even if you have only 1 short rest a day the fighter has him beat by quite a bit in terms of damage done before they lay down for the night.
Curing takes an action for the Paladin, which has an opportunity cost in terms of damage. For the fighter it is a bonus action with a much lower opportunity cost. From a pure math point of view, the Paladin can use an action, do no damage that round and heal 55hp and that is it for the day. If he heals in smaller amounts he pays in even more opportunity cost and less damage damage done to the enemy. The fighter starts will 11 hp more, can cure 16.5 with a BA (losing only his butt attack in this example) and will still damage the enemy for an average of 31.5 on that turn. 11+16.5 and 31.5 damage to the enemy may seem like a fair trade to 55 healed, but it is actually bigger than that. The fighter gets his 16.5 points back after a short rest, so if you have 2 short rests a day that is 49.5 points he heals himself plus the 11 more he started with is 60.5 to the Paladins 55. Over the course of the day if he uses all three in combat he also does over 90 damage on the turns he healed himself (not counting any other abilities) where the Paladin is doing nothing to the enemy those turns.
The Paladin I was using for this example has +5 to all saves (20 charisma) and has a lot of other abilities to boot which you can certainly argue more than make up for the damage, but I don't agree that he overmatches the fighter in melee.
For this example I am using a variant human battlemaster fighter, which has the highest nova potential and the pole arm master feat so it is an apples-to-apples comparison. That is probably not the way I would build a pure fighter in most cases though.
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