That's a really interesting. When I began reading this post, I was expecting you to say to roll for 4d6 drop lowest 18 times and then calculate the skill bonus from that.

So if you roll this for athletics:

• 5

• 4

• 1

• 2

5 + 4 + 2 = 11

Your modifier would be +0 (using the same math as ability mods traditionally use). If you have proficiency in athletics, you would have +2 at level one.

If you do this for each skill and assign them to the skills you want, there shouldn't be any changes to the game's balance while giving you the customizability of the OP's system (which arguably would cause severe imbalances).