TTGL is full blown mecha in the exact way you described to bore the shit out of you, and you seemed to really like that. NGE is centralized on piloting and fighting mechs too. The whole psychological trip is because of mechs and the shit the pilots have to put up with them. All of Code Geass's strategic movements revolve around piloting mechas. Canti is a big part of FLCL and its most memorable moments are during the climaxes of each episode. These are all full on mecha shows, take out the robots in any of these and you've got nothing. They'll show up when you search for best mecha anime. IDK what you're saying.
take out the robots and you've got nothing? are you kidding me? I like those shows for the drama, characters, and story, not the action sequences. I didn't even know TTGL was considered a mecha the first time I watched it because the robots are so unconventional. There is barely any "mecha" in FLCL at all; it's mostly a comedy and the memorable scenes are largely without Canti. You could replace the robots with aliens or some shit and it could serve the same purpose. No way it's a "full-on" mecha show. Most of what I liked about Code Geass was Lelouche's strategies in controlling situations rather than tactics in controlling mechas in fights. It's not centered around the action scenes as much as it's centered around the drama of setting up a decisive situation like chess. FLCL is hardly mecha, seriously. NGE gets called a deconstruction of the mecha genre; most mecha is absolutely not like NGE. The best scenes aren't EVA fights, in fact, I barely remember any real fights. There was usually just a principle that surrounded a character. The "mechs" were almost alive, too.
What defines the mecha genre is the focus on robots. I'm not interested in the robots themselves, and am thus not interested in what the genre's about. I've just liked shows that contained robots for other aspects which I've mentioned before. The most memorable scenes is Code Geass are absolutely not the ones where they're piloting mechas.
The whole "psychological trip" in EVA is not because of the mechs, it's because of the characters. It's not because Shinji has to "put up with" his mech, it's because he has to put up with himself and those around him. He has to take responsibility for himself and learn to let other people in emotionally. That was kind of the plot of the show. The AT fields were symbolic, among other things.
The "mecha" I like are extremely unique and atypical for the genre. Popular mecha that is more known for being mecha like Gundam, GaoGaiGar, and Getter Robo never interested me because they're too big on the robots. When the anime is focused around the idea of battles, it just bores me. I never watched Macross because I was under the impression that it was too much of a mecha thing. I've never watched Ghost In The Shell because it seems boring. I would much prefer the anime to be centered around something such as drama or sci-fi and be classified primarily as a drama or sci-fi, rather than have the primary classification of "mecha" because the main thing that stands out about the anime are the robots and how cool their battles are. Being part of the genre just seems to make the anime more boring to me because it's an aspect that I don't care for.