I don't think this argument holds up too well once you look beyond PHB. Strength is not the only primary stat for using a melee weapon. Swordmages and Artificers use Intelligence, Rogues and Assassins use Dexterity, all of whom can benefit from Eladrin Soldier. Eladrin Soldier can even help an Eladrin Wizard with the proper implement proficiency. Similarly, Dwarf Avengers get to use their high wisdom, and get the bonus from DWT.
And with Githzerai, we see the superior version of ES/DWT, which is probably what the Eladrin and Dwarves should have gotten all along. Really, at this point, can anyone explain why Githzerai get the +2/3/4 feat with arguably the best weapon group in the game? It seems pretty arbitrary, which makes it hard to argue that giving dwarven weapon training to a Dragonborn would be a major break.
Just to be clear, I'm not advocating this as good practice, too much loss of flavor for my taste, but I'm not sure I'd cry broken if someone did this.