What always has been relatable about Dean is he is not the character with the big supernatural myth arc. He was written and set up to be the normal one in the pairing - the one who kept everything grounded in reality. And yet he is a normal man who still had most of the pivotal events of season 4 and 5 revolving around him. In season 4, he is the one who get’s a special bond with an angel (not the brother who admitted to deep faith in season 1). In season 5, he's the center of the manipulation by the angels to get him to agree to be Michael's vessel, and during the time kills a number of major adversaries including the WOB and Zachariah - and all done by being fully human. The beauty of Dean's character is that he does all these remarkable things as a normal human, not some kind of supernatural hybrid like Sam.
Wanting him to have a big supernatural myth arc would be a denial of what makes his character so important. And I don't understand why some fans who clearly love him so much have such a hard time simply accepting him for what he is and not wanting to make him into something unrecognizable.
I'm going to be blunt here, because the complaints that Dean doesn't have his own story arc is really, really wearing on my last nerve. Dean has always had a very clear storyline of his own that yes, is often linked with his brother but still is his part of the story. What some fans here seem to want is his own distinct supernatural story line the way Sam has been given, but for me that kind of defeats the purpose of what Dean's character is about. Sam was the one saddled with a nasty Destiny (with a capital D), and Dean was the more relatively normal one trying to keep both of their heads above water. It was yin and yang and it worked.
As for the lack of storyline, let's look at the series so far...
Season 1 - Dean's storyline focused on pulling what was left of his family together and being the keystone for keeping them moving. He had his daddy issues and the season ended on a big cliff hanger with his life in the balance.
Season 2 - Started with John sacrificing himself to save Dean's life and then we began the Special Children mytharc. Dean's role here was unraveling the mystery around YED's plot and trying to save his brother's life. It ended with Dean making an enormous sacrifice in order to save Sam.
Season 3 - Dean's storyline focused on his crossroads deal and eventual demise. Sam's storyline was on the backburner for most of the season until the later part of the season, but the cliffhanger still ended up with the focus on Dean, having been taken to Hell.
Season 4 - This was the most singularly Dean-centric season of the lot. Dean's return from Hell, the introduction of the Angels (who were brought in attached to Dean's character) and his efforts to stop Lilith from breaking all the seals. For weeks, Castiel interacted with Dean and only with Dean. Sam was treated almost as an adversary and had no real role in the overall plotline except at the end when he killed Lilith.
Season 5 - This was Dean's supernatural storyline. He was the Michael Sword, and had his own Destiny. What fans seem most unhappy about is that the storyline did not conclude the way they wanted it. They wanted to see Michael take him and use his form to kill Lucifer. But we got the twist that Dean learned that doing that would doom most of the world and despite the enormous emotional pain he was in, found it within himself to tell Michael to stuff it, kill among others the WOB and Zachariah and embrace his destiny as a human and not an angel condom. At the end, he makes the ultimate sacrifice by giving up the person he loved most - his brother - to save the world.
Season 6 - Dean's overall plot has been dealing with the aftermath of season 5. He's tried to balance out a life with Lisa with hunting (which didn't work). He's had to deal with a brother who is not himself (to put it gently), and now has a new baddy on the horizon. He is trying to find his emotional equalibrium again.
Dean has had a very clear and distinct storyline throughout the whole series. Those who keep looking for him to have some kind of big supernatural destiny (like the theories that Death is grooming him to be a Reaper or that he now has permanent ties to the fairy world) are barking up the wrong tree. Dean's role in the story has always been the everyman, the normal guy fighting things that no one could imagine in their worst nightmare and doing it as a full human. So if you're looking for him to suddenly sprout angel wings or to be revealed a demigod, prepare for continual disappointment.