Ok, my bad. Just checking, especially since you also mentioned ASIs in the OP.
If you incorporated something along these lines I would you be applying ability scores and/or proficiency as well?
Example. Level 1, STR 16.
You roll d6 -3 and get a 2 (5-3) for Athletics.
Is your Athletics simply +2?
Is it Athletics + 4? (including proficiency)
Is it Athletics +5? (including Strength)
Is it Athletics +7? (including both proficiency and Strength)
Which way are you leaning?
I wouldn't mind such a system for non-proficient skills, where you would add ability scores. You could even roll them all first, and any that are really bad you might pick proficiency in to offset the penalty.