GiantOctopodes offers detailed breakdowns with actual numbers and statistics. In other words, game facts.
Dynia offers... fanboi opinion and emotional bias?
GiantOctopodes wins.
Dynia loses.
End of story.
Play what makes you happy

First, let me say that I'm not disputing the effectiveness of monks. I particularly like the class.
But in fairness, I'd make a few points:
1. Savage Attacker is better than implied, especially because the great weapon fighting style does not reroll ones and twos perpetually. It is a one time reroll, which is substantially helped by savage attacker, especially when additional dice begin piling up.
2. Precision attack and evasive footwork have to be considered more fully. As well as riposte. Short rests are not exactly hard to come by.
3. The comparison offered is based on the use of strength potions which is naturally going to favor the monk with the tavern brawler feat. The monk, without respec, simply doesn't have the point spread. This causes a heavy reliance on elixirs and potentially slot items that aren't necessarily needed by the fighter. For instance, while the monk needs either a respec or an elixir to make effective use of tavern brawler, the fighter could be using an elixir of bloodlust, granting even more actions.