It seems that the height of the camera in 1st-person view is not connected the character's height. At first, I thought this was because I used the "showracemenu" console command to change my race, and therefore the height wasn't adjusted appropriately, but after starting a new game as a High Elf, it appears to be the same situation: The eye level, or height of the camera, in first-person mode is about at the chest-level of the super-tall Altmer. When you toggle between 3rd and 1st person views, you can see an NPC who is looking at your character move their head, looking up at you in 3rd person view, and moving their gaze down to look at you in 1st person view.

Is this by design? Is there any way to fix it, other than wait for someone to make a mod to fix it?