|They add up fast! BTW, you can buy these on etsy.|
Right away I see the need to change the distribution so that the bonus comes at longer intervals, staggering them out so that you only see an increase every second or even third level. After all you aren't getting a +1 you are getting a +2.5 average. So instead of +1 per level you would get +d4 every second or third level. And because they would be staggered I'd want players to get some kind of advancement at each level so I would have to interleave skill bonuses with the magic level advancements and with the combat bonuses. Nothing worse than gaining a level and getting nothing for it so I would try to avoid dead zones. Since the skill bonus is pretty much the same as the fighter attack bonus, the progression would look the same, however it would ideally be spread out across the six skills. You would not likely have many characters with any single skill bonus greater than a 5d4. However the savant would break that all to hell and without some adjustment I can see characters with huge piles of d4s in a particular skill. In fact the savant class probably already bends the skill system as they can apply generous bonuses to any skill and there are no restrictions on pumping one skill up very high. Right now a 12th level savant character could have a +17 to any one skill if they ignored the others, however in a d4 system with the progression rate halved they would probably have a lot more than that since a modest 9d4 averages 22.5.
I'd not like to have arbitrary rules for this but it is possible that I could to make adjustments to limit skill bonuses to prevent problems, perhaps limiting a skill bonus by level number or something. This would further complicate the advancement to keep the levels balanced and I don't like unnecessary complexity. And if I have to do all that the question arises, what does this do to the game and is it worth the complications. Is having variable bonuses worth the extra effort? Then again, it might be fun to roll handfulls of 4ds. I'll have to try it and see.