So, again, we're considering the higher-damage melee types, not, say an archer or something. That's fine, just assume that they 'need' their armor & extra 2 hps/level to get in there and deal their damage.
Archers do more damage than cantrips. They also hide in the back behind cover (and other PCs) and wear their better than arcane caster armor and have their better than arcane caster hit points. It's a tradeoff. Damage for protection. You want the guy in back threatened less and hitting more, you get the wimpy damage. Pros and Cons.
And human variant fighter Sharpshooters are just plain nasty. They hit 50% of the time (8.98 DPR) instead of 75% of other fighter archers (65% against cover) of the time (5.85 DPR). The sword and board guy (+2 damage) is 6.4 DPR. The two weapon fighter is 8.8 DPR. The two handed greatsword fighter is 7.78 DPR. All of these at levels 1 to 3 with 65% normal chance to hit.
So, archers can have their cake and eat it too. As can other fighters who take variant human and a feat, but some of those feats only add a little DPR at low level.
Not so much. The Champion and Battlemaster have no dailies, and no one's taking an hour rest after each of 6-8 combats in a day.
That's why I said "Enccounter and/or Dailies".

But yeah, I call them Encounter abilities, but they are probably 3 times a day Dailies (4 if you count taking a short rest after a long day and you still have the ability in case of a bar fight or wandering monster that night).