It's not to push anyone over the edge. The new Cleaver is meant to favor AD Casters like Garen, Darius, and Renekton. They don't auto attack very often, only between casts, so the Rage passive helps them keep up. The CDR helps them use their abilities more often.
Then, Riot removed the flat penetration and some of the AD to make it less desirable to champions who frequently auto attack, like Riven or Yi. Champions like Riven with lots of dashes, or Yi with lots of MS, won't get as much use out of the new cleaver because the Phage part is much less worth it.
Think about the build path. In lane, Riven wants an early Brutalizer or Tiamat, either for the penetration and CDR, or the waveclear and auto reset. Phage brings nothing for her. The movement speed is useless, she already dashes everywhere. And don't make me laugh and tell me she'll build the Kindlegem first. Phage only gives 20 AD, compared to a Brutalizer's 25 or a Tiamat's 40. She'd be better off with a Pickaxe than a Phage.
If anything, this is an indirect nerf to Riven. Say Riven builds the new BC first. She'll have put herself behind early, because Phage doesn't give her that much power. She won't have as much AD than if she built Hydra or Ghostblade, so her shield will count for less. She won't have the penetration that Brutalizer provides, so her enemy laner can hard counter her build and outdamage her with an early Sunfire Cape.
No, this new BC won't make Riven an issue. She'll be the same as she always was, just getting a Ghostblade rather than Cleaver.
If it does prove to be an issue, riot will nerf her.