This is a terribly confusing situation all around. Takase is an insensitive asshole but he also definitely did not sign up for caring for a girl when he started playing with a neighborhood stray. Mii needs to be clearer about what she actually wants from the relationship or break it off, but she keeps fucking around when she should be firm and it just sends mixed messages about what she wants from him. Takase is a stupid jerk so it's on Mii to either lay everything out cleanly and let him choose or just hit the bricks and move on.
Yeah. I do think he could
learn to like caring for a girl, if the mangaka laid the groundwork for that (repeat "cudding as a cat -> transform into girl -> pull away quickly before he can reject you" until he's desensitized to it, maybe?). But whether that actually "works" is still entirely up to the author.
The problem is that whenever you have a romcom lead who has a deep mistrust/trauma toward humans/the opposite sex (take the female leads of Renai Daikou, for example) romantic developments are at the mercy of that complex. Whenever characters start to get close to each other, the author will just use that complex to restore their sense of distance.. The character in question can seem to just temporarily forget their trauma during an arc where they get along fairly well, only for the trauma to be resurrected arbitrarily later on because, for example, their faces got too close. The author is the only one who can determine the conditions necessary for it to be overcome, usually by their love interest doing or saying something that changes their perspective. But there is never a rush for this to happen... worst case scenario, it will only happen at the very end of the manga.
I'm not saying I can't like characters who have complexes like this. I like all the characters in Renai Daikou. But a lot depends on how much I trust the author. If we are applying real world logic, then yes, "maybe he's not ready for a relationship" is a fair judgment to make. But since this is ostensibly a romcom overall, I'm optimistic that they
will get into a relationship, even if it's only at the very end of the manga which always sucks.
On the subject of the other point you made, her behavior, I honestly don't see a serious problem at this moment. Yes, she's trying to use her crush's love of cats to get close to him, but that's just like a woman who dresses pretty to appeal to her love interest. As for whether she can turn that cat love into human/romantic love, well, she has no idea how to do it, and is torn about what to do, but the one thing she's clear about is that the one thing that connected them is in jeopardy, if he spends time with cats other than her... Of course, confessing outright would probably be counterproductive because he would currently just reject her and then it'd be awkward for them to cuddle as human and cat. Though regardless of what she says to him, the author can always manipulate plot elements to give them more opportunities to spend time together and for her to get to understand him and him to get to like her more as a human.