I agree with this conclusion. But the thing I find weird is that she would be trying to win Uta back for the wrong reasons. I don't think she loves Uta romantically, she is just emotionally dependent on her. I mean, could that be considered healthy? It would be best if she learns to stand on her own, and then, later on, decides on her own that she loves Uta, rather than out of desperation.
"Wrong reasons", and what is healthy can be rather context specific. Kaoru's needs aren't unreasonable - she isn't demanding constant attention/affirmation/compliments, or demanding Uta drop everything to attend to her, she just needs regular social contact & someone to "be there" when she is feeling low. She seems to be able to handle a day or two, it was long unexpected delays that seemed to be getting to her (and case-by-case relationship drama back when she was at school)... a lot of people "need" social contact at this level. The idea that everyone should be able to stand "alone against the world" is BS, humans are a social species (often it is just a storytelling technique - a way to "show" independence). But I do get the feeling if Kaoru left Reiichi her emotional support needs would actually decrease a lot, since his unreliability seems to cause a lot of her crises.
It is important to be aware of how you interact with others, and try to keep things healthy and balanced. Uta liked being there for Kaoru, her only problem was the pain/frustration of not being able to have more. Obviously Kaoru's initial attempt to get Uta to just deny her feelings was a selfish impulse, but longer term it is not unusual for people to re-evaluate their relationships when faced with change. Fear of loss can show us just how deeply we care about someone. She may come to the conclusion that her feelings aren't that far removed from romantic love.
I wouldn't put it past her to behave a little badly in the first instance if she is lonely/panicking (she already has, but maybe for a bit longer), but in the overall feelings are mutable and sometimes there isn't that much difference between "kinds" of love (in either direction). Cynically faking feelings to get Uta back, or trying to trap her back into the way things were would be bad, but pushing a bit trying to find a compromise, or re-framing her already intense love and "leaning in" to the romantic aspect instead of away from it could be healthy. Equally Uta may decide her platonic desire to care for Kaoru trumps her romantic feelings, and find a way to deal.
A plausible first conversion would be telling Uta how lonely she has been, how much she misses her and how much she means to her, with some apology and thanks thrown in... which could be seen as emotional blackmail, but on the other hand is basically the same as Uta did to her (dumping a load of inconvenient feelings).
I think the main reason for a break, leaving Reiichi some time before anything happens with Uta, is back to story telling again - it would make it clear that she left Reiichi for herself, because the marriage failed, not simply to "upgrade" (also avoid casting Uta as a homewrecker).