That's essentially what I meant by "incapable of playing piano". It's not just something he refuses to do, but an actual mental state that renders him incapable of playing the piano once, as you say, he gets into the groove. It's not a metaphor, as it has been repeatedly stated it being an actual mental trauma that he had suffered from.
How about when he finally makes the decision to enroll in a musical high school? Which essentially means despite him not fully getting over his mental trauma of playing, he realizes that he still wants to dedicate his life to music. I honestly can't see how that cannot be considered as authentic character progression.
Okay firstly, it is not implied, in any way, that he shrugs it off well. I imagine that his mourning was shown heavily off-screen, and it is something that we, as viewers, have no need to see. Secondly, assuming, for arguments sake, that the basis of his character development was not his own (and ignoring everything I've said previously), why does that mean his development should disappear after her death? Development is development,and real development sticks with you even after the source disappears.
I think the whole point of that scene was not to show him getting good at piano, but to show that, despite all the terrible things she did, his mother was still his mother. I'm surprised you never brought that up
While you are correct in that there is much lost potential in that matter, it was, in no way, the point of the story. The entire point of the story was to see how Arima develops from the beginning, a piano prodigy who is no longer able to play an entire piece due to his mental trauma, into a more mature person who, regardless of skill, not only regains his ability to play, but looks at music and his passion from a more mature perspective. Everything in the series helps him towards this; that includes his rivalries with Emi and Takeshi, his relationship with Tsubaki, his tutoring of Nagi, and yes, most importantly Kaori's health slowly deteriorating, which we are shown that arima relates to his own mother's death.
You seem to be forgetting the fact that she had that whole thing with her senpai, who she even tried going out with. It showed how she matured into taking relationships more seriously and being more honest with herself (which, let's face it, tsundere-like characters are absolutely horrible at). The example I mentioned is only one of the many intricate forms of development that her character undergoes, not only towards other characters but, yes, as you say, on her greater outlook in life.
I did say his development was subtle, so I concede in that point. It seems to me that he is, after all, a more minor character than Tsubaki, Emi and even Takeshi, so I'm not surprised that the series didn't give him much focus.
From everything you (and others) have been saying so far, it seems that a lot of the show's messages seemed to have missed the point with your interpretations. A lot of opinions I've heard have had very general views of how the characters acted and why they acted that certain way, and that being the case, I'm not even surprised that many did not appreciate it.
I'm definitely not the kind of person to say "you're just too dumb to understand the plot" and would rather find fault in the direction; if the viewer can't figure it out by himself, then that just means that the story didn't lead them the right way. Perhaps one reason is that they seemed to peg Kaori as someone more important than she actually is, perhaps to invoke a sense of pity from the viewers/readers, thus distracting from the internal development of the other characters, and linking her to everything else that happens throughout the story. Frankly, if there's any character that doesn't develop in the entire story, it's her