Hats- why the added hair?

I was going to wear a hat but they always change the hair style of my character.
Has a default hair cut....Is there a reason?
Blast goggles, glasses don't have this issue.

Because of attachment points. There's only so many points you can use to attach a costume part to a character, and the slot for "Hair" is shared with the slot for "Hats." Goggles and glasses don't interfere with them because they take a different attachment point (Face Detail 1). If hats were made into a Detail that could be used with your choice of hairstyles, they would a) have serious clipping issues with a lot of hair styles, varying between hats because they all have different shapes of brim and crown, and b) prevent the wearer from using the other things that take that attachment point, most likely Face Detail 1 or Ears.

While I'll concede it would be really, really nice to be able to color hair and hat separately - even if having "hat primary, hair secondary" ends up with parts of the hat being pretinted just so it doesn't end up totally flat - having hair and hat together as a single costume part solves more problems than it causes.

o.k...

As a simpler way of putting it, think of a City of Heroes character model as a Lego person. A Lego person is made up of several different interchangable parts - legs, pelvis, torso, left arm, right arm, left hand, right hand, head, hair - which can be swapped around, but you can only have one of each. So if you have a Lego person with no hair, that's one open place to attach a new part: either a plastic Lego hairstyle, or a plastic Lego hat, but once you attach one you can't also attach the other. City of Heroes has a more complicated set of pieces that come together to form a character than Lego, but the principle is the same: Once you attach hair, that fills the space that would be used for a hat, and vice versa. However, people don't want to have to be bald in order to wear a hat - which means we get hats that are combined hat+hair into a single part.

Is that clearer?

Spot on, Flashtoo.
The ideal we could hope for is to have each hat come with some hair options. That's no small task as it requires each hat to be made individually with however many hairstyles, plus the User Interface work to provide those options.

Still, I'd always hoped they would do this: Hat - with no hair, with short hair, with medium hair, with long hair

You'd never satisfy all wants/needs, but even just with No Hair, Short Hair and Long Hair, I think it would be an enormous improvement.

Still... thems a lot of hats...
And they haven't done it, for all this time, so far...

Hats are hair man!

Clicking on the linked image above will take you off the City of Heroes site. However, the guides will be linked back here.

Maybe they could apply the same tech that lets us color the inside and outside of a cape separately to color the hat and hair separately? Replacing the skin tone tab with a second color tab?

Though I suppose they'd have to remap the colors on all the hats...