Everyday men are concerned with power. It's an aspect of our gender. Gendo is no different, especially at the end of Q, sitting atop inarguably most powerful structure. He's possessive with both Yui and her subpart Rei.
Shinji is the prince of the new series. Certainly a lot of bad things happen to him, but surrounding him are powerful supposedly-inconsequential events. Chaotic ones, sure, but powerful ones no less.
- Shinji pilots a giant robot exceptionally and is able to use it's functions not only to help humanity but also to fight other species. He didn't have to engage in a lot of combat situations to get good at it either.
- Shinji has many supernatural events happen around him, where he makes it out physically OK. Turning Unit 01 to "Automatic Battle Mode" in a severely-outclassed fight(Dummy system on Asuka) saved his life. Phasing out of time and space for 14 years is an OP feature.
- Shinji is a trigger to catastrophic events. He's like an unarmed nuclear warhead: useful when deployed.
- Shinji didn't need to earn his stripes to be useful on a team. His robot, his career, and his lifestyle were all given to him. Asuka makes note of him being daddy's boy but she's not wrong.
It's true that these events aren't necessarily endorsed by Shinji and they merely happen around him, but regardless Shinji is a character that benefits from many of them. Further the ones that don't benefit them are an extra half point because they don't remove the power surrounding him. Shinji goes through a lot of psychological trauma but most situations play out with him still being in the next scene, in one way or the other. He's the golden child. Technologies are built around him to allow him to survive because he's such an important piece.
Is Gendo jealous of this, even though he uses Shinji as a pawn in many of his maladaptive schemes? There's no real features of it in the new series and in the previous one we were left with Gendo releasing heavy guilt as he was crushed by Unit 01. What do you think? And if it's there, do you think it may play out in Final? Speculatively, if Shinji grabs the symbolic crown in Instrumentality, will Gendo push Shinji to the side?