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I'll share some of my personal thoughts on duel scaling champions, but these are just my thoughts.
I think it comes down to a per champion basis. We see many champions have multiple options of build styles (Tank, AP, AD, bruiser, enchanter, etc) when these styles offer something different.
Malphite, Gragas, Amumu, and Singed are all tanks with AP builds. The important thing to take note of is that these builds offer something that their tank builds don't. They play differently, and have noticable trade offs.
We see similar things with Seraphine, and Lulu with their mage builds behaving differently than their enchanter builds.
But AD and AP builds are a bit different in that typically these builds have the same or very similar goals (do damage) and the playstyle of champions trying to have both options tend to not change their playstyle between them. So it's harder for these to feel interesting when AD and AP builds have the same output.
AD Kai'sa and AP Kai'sa play very differently, and different situations where they are strong. AD and AP Teemo, and Shyvana are in similar situations. But many others tend to play the same, just with different items.
I personally think this is healthy.
In the cases where this changes the damage type of a champion (ex an AD build dealing physical damage vs an AP build dealing magic damage), it can be confusing when a champion you expect to deal physical damage suddenly swaps to being primary a magic damage threat. Avoiding this helps avoid extra unnecessary complexity.
I'm also strongly of the mind that AP and AD builds should also feel different. This helps give mages, marksmen, bruisers and all dps classes clear directions for where they are powerful/weak and should be picked. This also makes sure classes and champions within those classes feel different.
But why do champions have duel scaling? Part of this is historical from when champion kits where older and bits of incidental AP and AD were floating around. Or some hybrid items were a larger (though never very large) part of LoLPC. Having nonstandard scaling (Shyvana typically builds AD, but her 2 scales with AP) allows us to put more scaling power into other skills and still let the odd skill out do its job.
However there are some champions/builds that we like to support because it's something that supsets of our player base enjoy. We don't expect them to be the primary build for these champions, but if we can it's nice to keep them playable.
Sorry for any typos, writing this from my phone.