There are many things that are wrong with Skyrim ( Oblivion and Morrowind too ) 's First-Person view.
Let me list these things.
1. You cannot see your body , you're just a flying camera with hands.
There are mods for that , but they will never reach playable state in my opinion.
For an immersive game this is a huge disappointment.
2. Forced switching to Third-Person mode.
Horse riding , Mounted combat , Vampire-Lord , Were-Wolf.
All these force you into Third-Person mode , very bad.
3. Heights in First-Person mode.
Your view from the First-Person perspective is locked at the neck ( Right ? )
So no matter what race you play , you will not see any height differences in First-Person mode.
I'll add others as I'll recall them.
What do you think ?