Well look at it like this. How many dwarves have you seen using dwarven waraxes. Ok, now how many NON-dwarves have you seen use it.
Now, how many different characters (and thereby races) have you seen using the battle-axe? How many dwarves?
Now, to determine if your campaign needs dwarven waraxe as a weapon familiar to dwarves just compare those results to what you want them to be. For instance, if you find a lot of non-dwarves take d. waraxe and dwarves dont bother, then perhaps giving it to a dwarf for free will make it more prevelant among the correct "favored" race.
Do you have an axe-heavy campaign in general? Maybe you have orcs that go for battle axes and shields over greataxes, and other races using battleaxes, so its nice that the dwarves' have their own axe which they prefer to use.
Personally, I don't think I will allow it for my dwarves, not without some sort of "nerf" on one of their powers (perhaps changing the +2 vs spells and spell-like effects to be against something the dwarves encounter often, conjurations perhaps). I will allow the dwarven urgosh as a racial familiar weapon though.
Also, personally, I will be granting the orc double-axe to half-orcs raised by orcs. They don't really need a "nerf" counterbalance, and its a double weapon besides.
Re Elite: Its still elite, now all dwarves are considered to be elite axe-wielders compared to humans, elves, and other races who must spend a feat to use the dwarves' axe. Although, as I said, I won't be using it without nerfing something from the already-house dwarf.
And, I do like the difference between dwarves' and elves' weapon proficiencies.
Technik