The on hit problem:

First problem: On hit effects don't synergise with items at all. Champions who have on hit spells in their kits do not get to proc a number of items who proc on spell damage. This makes building raw scaling a much stronger build.

Second problem: On hit items don't synergise at all. The two main on hit items used today are (AS, magic damage proc) and (AS, physical damage proc). Starting from these two items, there is very little further a build can go, past buying a bunch of AD / AP / AS.

Finally: Champions who have strong on hit spells tend to have scaling which does not work well with a traditional build of pile on on hit effects.

My solutions: We change on hit spell damage to proc like spell damage. This means and are proc'd.

We change the best applier of on hit effects to apply all on hit effects as if it were a full attack. This means Fishbones splashes and Kayle E splashes, Teemo E burns and Kog W shreds.

Finally, we alter to have bonus AD, AP and bonus AS scaling damage. Thus, each bolt would do 10 + 0.X Bonus AD + 0.Y AP + 0.Z Bonus AS damage. Building either of the two main offensive stats to scale your on hit skill, as well as building AS to apply them more often.

Thus, we come to our final on hit (example) build:

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This will provide: +187% AS. +190 AP. Hp, Magic resist. Two extra on hit procs per attack.

On hit, you will gain: 43.5 magic damage from nashors, damage from new scaling hurricane, 5 MR steal, and 12% MS for 2 seconds.

On spell hit, you will additionally gain: 15/35% slow and 12% current Hp burn over 4 seconds, as well as spell effect.

This is enough of a pile of steroids / on hit effects to make an on hit build for champions like Kog, Teemo, Kayle viable.