Riri's feelings may be genuine but they aren't at all reciprocated. Nanjou made it clear that she will always like Hayama-sensei, but rather than accepting that, Riri wants Nanjou to confess for the chance of being rejected and having a chance to be with her. Now it'd be something else entirely if Hayama-sensei had no interest whatsoever in Nanjou, however that doesn't appear to be the case as Hayama-sensei does seem to share similar feelings with Nanjou.
That backstory made Riri even more unlikable in my eyes. She even admit herself what she's doing was useless and borderline obsessive. Hell she was second away from wishing for Nanjou being rejected so she can console her. How can you pretend to love someone when you can't even wish them happiness?
Honestly, the way Nanjou responded to her constant aggression show just how mature she is. The nurse just got herself a gem of a girlfriend. I hope, for Uda's sake, that Riri will get a massive redemption arc. Otherwise, saddling Uda with Riri would be a crime against all things Yuri.
But wasn‘t it shown that Riri understands that It‘s wrong for her to wish for Nanjou‘s failure? It‘s just a feeling she had, she doesn‘t try to condone her desire or act on it.
Also, If I’m not mistaken, Hayama-sensei haven’t really tried to encourage Nanjou. For the longest time(prior to final year) it was just president’s one-sided show of affection to her school nurse, an authoritative adult, who is ought not to respond to such feelings of her charges. So, president too was an example of someone desperately clinging to her love, even though it might be quite troubling and hopeless.
I think romantic love usually means that you wish for mutual happiness, and may believe that it is you, who is able to provide that very happiness to the significant other. It might not be so altruistic, and could likely require personal considerations over feelings to reach some sort of selflessness.
As I see it, Ruri seems to finally come to terms with her feelings: she still loves president, It’s her honest feeling, but is content now with not having her love reciprocated.