It's not like she can tell the other two that only she can be the center piece. Of course now Kana said she's not interested, but Ruby is actually a pretty idealisic, naive girl, so it might be difficult for her to give her all as the main idol of the group if she knows Kana is actually much better and more deserving. MEM, however, is as serious as Ruby is, so she can't simply be pushed aside. They didn't join to merely become Ruby's helpers or sidekicks. If Ruby wants to be the main girl, she needs to beat and convince the other two.