That's a natural part of a relationship so they should do it at some point, but I don't think they "need" to rush it or something.
Thay are building feelings and trust towards eachother, that's what makes it different from her previous "partners" who gasslit her into thinkg that agreeing to sex right away is only thing for her to be valued/loved.
Honestly, at this point, I don't think they are rushing it too much. This is a natural extension of their relationship. They already trust and very much like each other....maybe her more so than him, but he still cares very deeply for her. At the beginning he was hesitant, but as time has gone on he has come into his own and this relationship.
The whole thing with the ex was definitely weird, and he freezing up when he touched her and his inability to do anything was definitely not a good thing. I do think his response to run, while not the best, was also not bad. He took her away from a situation she felt uncomfortable in (which is probably why she froze up), sometimes you can't ask for more than that. Him pulling her away like that and being possessive (and protective) of her is one part of why she loves him deeply. She recognizes her relationships prior to this were not real relationships and just flings for the guys she was sleeping with. They valued nothing and really if it was any of them they probably would have just let her go, but not MC.
Nanjou is locked in on Kiyomi and wants to be with him for the remainder of their lives. If things continue this way they will just fall deeper in love as time goes on...so I should probably stock up on Insulin.