If this game is only about killing dragons, then I'll skip it. However, I think it is really going to be much more than that.

YES. I have seriously started over SEVERAL times because i didn't like the way my character looked.

Yes, if done right. It wouldn't be right to have a barbers shop just on some street corner, that just seems out of place... instead maybe something like a young farmer who needs practice before shearing his sheep

Yes this may happen... but do you all play 3rd mode or what ?
In first mode i see my character like 0,05¨% of the time, only when in menu to see how an armor/weapon fits.

Seeing how there is first person and third person options it's only reasonable to assume some play in third person alot more than others and the other way around. Your play style does not define everyone elses, such is the way of TES.
On topic I would like to see this and even growing hair probably could have been done in oblivion since there was a length slider they maybe could have made a script that alters that value as time progresses so it's a possibility for skyrim.