Item Procs on On-Hit Abilities

It's been something that's puzzling and very confusing for many over the years with the additions of items like Luden's and Liandry's that proc off spell damage. Rylai's was always explainable because it was such a powerful item, yet Riot recently buffed it and many champions are able to keep enemies permaslowed at a range with the item. Like Kog with his R or simply managing his CD's well, Kayle's AA's, Ahri, Malz's E, Zyra throwing down plants, etc. So why do we keep things like Teemo's E, Kog's W, Varus's W, and other magic damage on-hits from proc'ing these things? Kayle's E has always proc'd the spell damage items and still does and it's conceptually the same thing, an on-hit. There's also Fizz's W. The initial hit of Fizz's W, the activation, doesn't proc the spell effects, yet the DoT on the passive DOES proc Liandry's and Rylai's as well as Luden's, kind of an oddity.

It would be nice if the whole on-hit thing changed so it wouldn't feel so silly and backwards. I mean, Kayle is pretty much the only one who gets the proc these things doing the same exact thing as the others. Auto-Attacking.