Of all the reasons that people give for why Yellow Diamond was the one that shattered Pink Diamond, possibly the most absurd one has to be that she did it to increase her own power and control over Homeworld and so she could increase the number of planets she personally had.
Because, seriously, has Yellow Diamond ever been shown to crave power at all? To want more gems and planets under her control? If that were true she would have taken Earth as her own. But she doesn’t. She wants to destroy the Earth; to put the pain it represents behind her.
And her actions towards Blue Diamond also show that she has no desire to increase her own personal power at the expense of others. Blue had been neglecting her duties because she was so busy mourning Pink Diamond. And Yellow could have easily taken over the planets and gems had. Even if she still kept them technically under Blue’s domain, with them continuing to wear Blue’s colors and all, she could have easily taken control. After all, the Diamonds are all seen as perfect, infallible leaders. If you’re a Blue Diamond gem, and Yellow Diamond appears and says, “Do this”, are you going to disobey her because she’s the wrong Diamond? Of course not.
Instead, Yellow goes to Blue to convince her that she has to go back to being a leader, to being what Homeworld expects of her. There is no attempt to take over Blue Diamond’s power and authority. Rather, there is an attempt to have Blue Diamond take her own power and authority back.
Honestly, that whole idea seems to based on there must be a bad guy mentality, and that “bad guy” must do typical bad guy things. And what’s a more typical bad guy thing than killing for power? It’s positively cliche. But Steven Universe (the show) has never done cliche bad guys doing cliche bad guy things, and I can’t see it starting now.