Well, let's just say that the Great Retcon never happened. Let's say we go with your "have two versions of a champions lore, why they're fighting on the Rift and what they're doing outside the rift". Okay, where does the story go? Characters keep piling up and piling up and piling up, yet remain unused. A very small minority of characters would actually become less interesting in my eyes, if they were forced into the League.
Let's take Rek'Sai. Under League's old handling of monster characters, she would be locked up in-between matches. That presents a few problems for me:
- Her lore would feel very much the same as Cho'Gath's. "Big monster gets locked up because it wreaked chaos". Except she'd be dumber than Cho... no charisma, no planning, no depravity; just animal fury.
- She wouldn't be prowling the desert, a scourge now as she has been for decades. She couldn't inspire that soul-crushing dread into people who realize that she is after them. It'd just feel like, "Well, there's dangerous bugs here in this region, but nothing that can't be handled."
- The culture that has sprung around her and the other Xer'Sai, of using disposable bell boys to distract the Xer'Sai, would feel weak. If random League Summoners could subdue her, why hadn't it be done before? Noxus had summoners, since in the old lore everyone had summoners of their own, and Noxus hoped to capture Rek'Sai for the gladitor pits (as seen in her supplementary lore). So why hadn't it been done?
Not to say the new lore is absolutely fantastic and the old lore fans should just shove it. It isn't, and they shouldn't. But these are just my two cents.