Hybrid Champions: Was There Ever Any Intention?
Riot has played around a lot with hybrid champions, and there are viable ones like
Hybrid champions run into a few major issues though.
First: item scaling.
If you get AD, AS, Crit, Armor Pen, and life steal: each stat multiplies the effectiveness of all the others, resulting in 2 x 2 x 2 x 2 x 2 = 32.
With AP, Lich Bane, M Pen, Rabadon's: same deal.
With AP and AD stats: it's just a 2 + 2 + 2 + 2 + 2 = 10 road. AP and AD have no innate synergy with one-another, resulting in no real drive or incentive to invest heavily in a late-game hybrid build.
So no champions invest in a late-game hybrid build.
Many champions get 1 hybrid item to start with like 
to ride the early-game powerspike and adjusted cost-effeciency of such items due to needing to be cheap early to offset their lack of scaling late, but pretty much everyone stops at 1. Once you get into 2 major item core builds you start loosing power from grabbing 1 hybrid item, and you loose a ton of power if you maintain a hybrid build 3 major items in.
Secondly: the in-game implications of hybrid damage, counterbuilding, and on what champions it's useful on.
Pure-damage carries are pretty easy to target with counterbuilds at the moment, with armor items targeting auto-attacking (
) or with MR items countering more ability-centric things like burst damage, CC, AoE, or long-range poke in (
)
When it comes to hybrid damage split between abilties and auto-attacks though, sustain and burst: there aren't any good defensive items that hit everything, and as physical, magical, auto-attack, and ability damage all completely ignore half of the effects from a range of defensive items.
Ultimately the combination of bad offensive itemization and poor counterbuilding defensive itemization with Hybrid damage favors champions that need to do relevant damage throughout the course of a game through bases, and is pretty anathema to champions that actually need glass-cannon offense with AD and AP.
As such: hybridized damage that mixes physical, magical, auto-attack, and ability damage is extremely common in a wide range of predominantly HP scaling champions in:
So: it's not so much hybrid champions don't exist, it's just that hybrid damage is set aside for champions that simply won't itemize heavily in damage.
In the case of most of the champions listed: AD and AP aren't terribly cost-effective, and it's much easier to rack up damage from items that just offer physical or magical sources of damage that specifically aren't AD or AP in items like:
Tanky DPS: the true hybrid champions.
to name a few.
and old 
