First, that any fighter in the party will probably have acquired a much more powerful magic weapon by then which would boost their damage considerably
to make up for a 14 point deficit? A flametongue would do that, but the bladesinger could have a flametongue, too. The bladesinger is getting three strikes, here - just like the fighter is, and they have a better damage bonus than the fighter (+10 instead of +5),
and can lay cantrip damage on top of that.
Its a reasonable assumption that if the DM will change the rules to allow the bladesinger to dexify and PAM a stave, they'll give them nice magical ones, too.
And second, since the bladesinger is indeed still a wizard... by 14th level there's always a good possibility that the character at that point has begun using their attack rounds to cast spells for damage or other wizardly control purposes, rather than still weapon attacking each and every round. Thus the bladesinger's melee damage is no longer is as important to him as often as it might have been at a lower level. At which point trying to compare the bladesinger to any other warrior in the party ends up not being that useful.
You're right - they're still a wizard. The class with arguably the most options and versatility in the game, only in this case with a subclass that already has great at-will damage has even better at-will damage. Good AC, tons of slots for shield and absorb elements, and Song of Defense. It is a strong subclass, and this is a straight damage upgrade for it - just as it already got one (the TCoE cantrip/attack change). It was good before, it's great now, and it doesn't need more.
In this case the bladesinger can absolutely hang with the fighter, blow the rogue out of the water (with at-will damage, too), and still do all their fun wizard stuff; and because of how PAM works there's no conflict with somatic components and dual wielding to get that bonus action attack, nor is there any startup time like there would be with Melf's Minute Meteors or Crown of Stars (and they don't have to spend any resources, either, other than bladesong). And all of that is before considering how easy it is for a bladesinger to gain advantage relative to a fighter.
It is a strong archetype for a strong class - and this is a buff that interacts with the subclass's strengths in a strong positive way.