I don't accept that premise...and neither does WotC. Nor do 5e tier lists. In fact, fighter is usually one of the higher ranked classes. Which is why fighters are getting new options but not power buffs, aside from those they will share with other classes via weapon mastery.
When it comes to just DPR, fighters are arguably the S tier class in 5e, and certainly in the top three. That's not where they need help, and buffing their damage would absolutely unbalance the game.
1) Popularity rankings are not power rankings. Fighters are popular because 80% of all fantasy heroes are martials of some flavor or another, not because they are the strongest class in the game.
2) DPR is not the main way to measure power in DnD. It is notable that anyone who does guides for spellcasters always seem to mention that building caster DPR is a waste of their potential, and blaster mages are the weakest way to build a mage.
3) Even if DPR were the main way to measure power in DnD, fighter's are only good at Single Target DPR, the weakest type of DPR, and if you start allowing for AOE DPR, casters are usually doing just as good if not better than fighters. As are paladins, which are half-casters.
4) No one said anything about buffing fighter damage. They talked about buffing the fighter. There are ways other than damage to buff something.