It goes a bit further than that. You've got three ponies on each side who are outstanding examples of their race's special traits, and three who are unique and unusual exceptions.
The Exemplary Three:
-Unicorns are known for magic. Twilight is the most powerful magic user shown so far (among non-princesses, natch.)
-Earth Ponies are known for affinity with the land. Applejack is in charge of Ponyville's biggest farm and knows all there is to know about growing apples.
-Pegasi are known for flight. Dash is a Best Young Flyers Competition winner and the only known pony to ever perform a Sonic Rainboom.
All three are highly devoted to working on these skills, which they would not be able to have if they were any other kind of pony.
Then there's the other three. They are all exceptional examples of iconoclasts: Ponies whose talents are NOT related to their race.
The Exceptional Three:
-Rarity designs clothes. Every other fashion pony we've seen is an Earth Pony. Even her trademark accessory, gems, come from the Earth, which may mean that while she needs magic to find them, an Earth Pony might be able to find them intuitively.
-Pinkie is a baker/party planner. Not only are these things unrelated to an Earth Pony's powers, her hyperactive, quick movements make her seem much like a Pegasus, and her ability to bend reality to her will implies magic, a unicorn trait.
-Fluttershy works with animals; almost exclusively LAND animals. Despite being a Pegasus, she tends to walk more than fly, spend her most of her time on the ground, and even has an ability to communicate with the creatures better than most. She explicitly says she wants to "never leave" the ground when she first discovers it. She has more Earth Pony traits than Pegasus traits.
There really is an amazing balance among the mane 6, in several ways.