As far as I understand the term, "flat math" indicates much smaller numbers in the attack / defense department, not in terms of damage values. The WotC developers have stated they intend for damage to increase by quite a bit so that low-level monsters with low HP become mooks because they die in one hit. Giving the fighter the ability to double his damage output seems consistent with this.I couldn't disagree more. Multiple attacks make a mockery of flat math. They mean, not to put too fine a point on it, that a 6th level fighter is more than twice as damaging as a fifth level fighter. So much for flat math.
However, you are correct in that there is a significant power increase at sixth level for fighters in 5e. This was partially mitigated in 3e by the penalty on iterative attacks. In order to "solve" this dilemma, I recommend bringing back 3/2 attacks.