Sorry so late on the response, was in class last night.
As a Druid main, I do still tend to care about how my Druid looks, though part of that may be as I tend to go more towards Resto & Star form. I'm still going to be seeing that character's look during cutscenes as well as when I first log into the game. Especially that first log in, I get to see him surrounded by his home area wearing the gear he has earned in the tabard I've chosen for him for that particular expansion. I know the other forms will cover his look, but his base look is the one that really ties me to the character.
On a Dracthyr, that's a bit different. Their base look is one that I can update at the barber shop, but not one that shows what they have attained or the like. When I see my Dracthyr on the login screen, it will either be a dragon-like creature that was rendered through customization options & shows none of what they have worked towards or it will be a visage form that does show some of what I've done, but is in lore the disguise to who my character actually is.