Hybrids have never really "worked" as a concept. You've always run into one of three cases.
1: The hybrid champion is good to great when built to one particular strength. I.E. Jax building like a bruiser and kayle building full AP. The reason for this varies. Sometimes it's steroids, sometimes it's ratios, sometimes it's just having a functional kit with a balance of the former. The hybrid is generally far weaker in their other build options (AP jax, AD kayle), generally either extraordinarily bad or noticeably below average.
2: The hybrid champion is awful to poor no matter how you build them. A good example is Kayle in (I think late s4?) when she had all of her scaling hit, all ability ranges dramatically nerfed, bases nerfed, and some base stats nerfed.
3: The hybrid champion is poor to average no matter how you build them, however there is one particular item which has the perfect amalgamation of stats to make them strong. I.E. Jax stacking gunblades for that short while where they made the passive stack and heal for any damage (physical or magical) done.
Basically, hybrids are gimmicks. They're only function with one particular build (Jax is a bruiser carry, Kayle is a mage with some utility and some of her damage in autos) and are occasionally, unintentionally, made horrifyingly OP due to some unforeseen interaction with an itemization change.. Which leads to the champ, or the item, being nerfed.
EDIT: It's also worth noting that things like old Yi, old Poppy, and old Sion weren't actually hybrids. When League was first released - and for awhile after - the idea was that AD would only effect auto attacks, AP would only effect abilities.
Early on in league, melee damage champs were just awful. The only ones worth anything were mages (morde) and tanks, the rest were garbo (wyndmere phases not withstanding). AD scaling was one of the things which was implemented in the "everything and the kitchen sink" methodology of trying to get some melee champs who could function beyond being mages or tanks, this is what Irelia and Xin represent.
Eventually Riot realized how poorly it worked and now you have champions who generally have their ability scale with the proper thing, but older champs who haven't been given immense Sion level reworks tend to have elements of this in their kit.
This stuff tends to get taken out because, due to how bizarre a design choice it was, champs who have it tend to be very gimmicky when built that way. I.E. old AP Tristana having some impressive burst, but just about zero damage outside of her ulti and having to use her escape tool as a drop-kick nuke ability to actually kill people.