the thing about akechi is that you need to filter everything he says and does through the lens of "he hates himself." as in, he absolutely loathes himself and believes he is fundamentally worthless. it all goes back to his original sin of being born. he believes at the core of himself that he's a plague on society and specifically on his mother. it's both his fault that she died and that shido abandoned them.
so, everything he does and says is to cope with this fundamental self-loathing. when he acts remorseless, it's because he already believes he's an irredeemable monster just by existing, so why should he care? when he acts regretful (such as in the engine room, but there are other moments as well), it's because his worthlessness has been confirmed by his failures to be a good person or succeed in his revenge. when he expresses a desire to be a hero, he has to view it from a lens of external validation, because he does not believe he's a hero or ever could be one--the best he'll ever get is appearing to be one to others, and he uses this as a mask against the self-loathing. if he pretends hard enough to be a different person, maybe he really can become someone else who is worthy of love.
it is all extremely self-centered, but that's because akechi has the psyche of a child who thinks of himself as the center of the universe. everything horrible that has ever happened is his own fault, everything good that has ever happened is thanks to his own cleverness.
you can't really make moral judgements on his remorse or lack thereof when the reason he behaves one way or another is not due to a lack of care for others. it's due to his view of himself. he can't and doesn't extend his perspective beyond himself because he's not been given the tools to and he's been so isolated for most of his life that there's no one left, until joker, for him to care for.
he does care for others, though. just look at how he feels about his mother. the origin of all of this was his desire to save her, because he loves her so much. and because he felt like he owed her and it was his fault she was suffering, maybe, but that complex emerged more after her death and he blamed himself for it.
statements such as akechi "feels no remorse" or "doesn't think he's ever done anything wrong" are short-sighted because they're taking his words and actions at face-value. he may claim not to care, or act like he has no remorse, but examining why he says and does these things reveals that how akechi really feels about his impact on others is irrelevant. he doesn't even know what he feels about what he's done to hurt others, because he doesn't let himself get that far. and his "fuck society, they're all corrupt, let them all burn because there's no such thing as a good person anyway" mentality helps a lot with his denial of the negative consequences of his actions.
akechi very much knows everything he's done was very wrong. he says as much in the engine room and in third semester. akechi knows he's a monster and has done terrible things, and he did it all anyway, because he doesn't think he is capable of doing anything that could make him a worse person than what he became when he was born and ruined his mother's life.
