Not to discredit your reading but I never really got that impression from the show because it didn't feel like it was commenting on the same kind of issues.
For me, the main theme of Kuromukuro was self-determination vs control. Most of the key characters, at some point, had to consider the societal/organisation structure that was binding them to live their lives in a certain way and ultimately reject that structure/organisation. This wasn't really a theme that Evangelion dealt with.
What's interesting about this theme is that I don't seem to recall many anime directly attacking the oppressive nature of Japanese society. For example in Kuromukro, the structures that are criticised are alien races/military bureaucracy which exist clearly as stand-in for Japanese society. Harmony does a similar thing where they critique the controlling nature of the system, but that feels like an even more transparent attack on Japanese cultural/behavioural norms.
Of course, it's hard to really comment on or decipher these ideas as an outsider to Japanese society.
When I say "in certain respects" what I really mean is "the relationship between Yukina and her mother."
So our starting point is traditional 70s-ish super robot anime. The hero is a teenaged boy who works alongside his scientist father, sometimes posthumously, to have these hotblooded robot adventures. They don't always see eye to eye on everything, and may have been distant for a period, but when push comes to shove they put their differences aside to fight the bad guys. Reluctance to fight on the part of the hero is rare and usually not a major focus.
Then there's Eva. The relationship between Gendo and Shinji is fundamentally broken and abusive. They've been distant for years, and that distance continues throughout. Shinji is (as expected of a realistic modern Japanese teenager) scared of death and violence and doesn't want to fight. Only through emotional manipulation (first the implied threat to Rei, and then dangling fatherly approval) does Gendo convince him to pilot. As the series goes on their relationship, and Shinji's mental health, deteriorates from clashing philosophies and combat stress.
Finally, Kuromukuro. It genderswaps these two archetypes, for one thing, which probably merits an essay of its own, but that might be beyond my capabilities. There's some workaholic stuff played for laughs, but compared with the previous scenarios Hiromi has been much more present in her childrens' lives. Yukina is initially as scared of combat as Shinji, but Hiromi never tries to force it on her, even telling her that she doesn't need to be a pilot anymore. Yukina is ultimately able to decide on her own that piloting is a responsibility that she needs to fulfill, rather than doing it for the approval of another. And finally, near the end there are several instances where Hiromi prioritizes her daughter's wellbeing over loyalty to the UN or its mission.