If all skills were set to start at level 1, how would this impact the game in terms of levelling.

The potential issues that i can think of so far are

• Would levelling become quicker
  
• Would the player get to maximum level without having all skills at 100
  
• If (2) is true, could you still level skills upto 100 even at 80

Are there any other potential pitfalls?

0) Use a legible font, please
1) Leveling would be quicker at the beginning
2) The level cap only exists because that's when you hit 100 in all skills. Would starting at 1 be enough to raise the cap by one or two levels? Maybe.

With all of them, you'd be halfway to level 82.

Use http://skyrim.nexusmods.com/mods/1175 and let all doubts be gone.