I like Genesis as a character... but it took me watching the JP version of CC (ENG Genesis sounds... very jarring compared to JP Genesis), a lot of research into all the background details we see in the final Banora Caves dungeon, a lot of mentally mapping out "how did a person who was like this as a kid turn into this kind of person as an adult", and comparing a lot of JP anime/manga-only archetypes/themes to Western archetypes/themes for me to like him.
Aside from CC's sloppy execution, which... effects a lot of things other then Genesis in CC, what I think Genesis suffers from the most is that CC has... a lot of themes and character archetypes that don't really have a Western counterpart. This is most obvious with the whole "company loyalty" that Zack and Sephiroth see Genesis as betraying. It's... really hard to sell that idea to a Western Audience once they figure out that it's Shin-Ra that experimented on Genesis (and everyone else) in the first place. And it always bothered me that "Shin-ra is the source of Genesis degradation" never became a major plot point. Instead it's Zack wondering why Genesis would betray his two friends who are still with the company and Sephiroth having to deal with why his best friend left him. Genesis himself never flat out says why he left either mind you, although that is slightly more understandable as it is canon that degradation means your mind starts breaking down just like the rest of your body does. He also might have thought it would be obvious to Sephiroth as Sephrioth grew up with Hojo and... all the main characters would have gone though the process of becoming SOLDIER. They all know Shin-Ra messes around with doing weird medical procedures on people long before the game starts.
The other archetype is Genesis himself. Western media doesn't have a lot of... really powerful fighters that are interested in things like... old literature and are still portrayed as being really awesome fighters. Traits like "expert on old english lit" are usually seen as things that make people weaker and don't contribute to them being good fighters. So they're things to hide rather then show off to war buddies and see them laughing with the person about it. Where you do see that kind of character archetype is in... historical JP anime/manga. There's a number of samurai -type characters where "really good at all that poetry stuff" is part of their character archtype and no one gives them any grief over it. There's also a lot of samurai characters where being obsesed about their honor is really important to them to. And Genesis (and Angeal) would feel right at home in those types of anime/manga. They're pretty much varriations on samurai archetypes that genre-hopped.
The other thing is... a western movie has pretty much Genesis' character arc in it... but from a western mindset. The Borne Legacy is basically Genesis' character arc. You've got a super-soldier who got experimented on by the organization he works for and is now suffering bad side-effects from that experimentation. He leaves the organization and goes to find the scientist who came up with the experiments done on him. The scientist eventually says they can fix what was done to him and leaves with the super-solider. Meanwhile, the organization the super-soldier left start sending super-solders to track him down and they chase the defecting super-solider and the scientist with him. This is when the story splits based on how it "judges" if the defector was right to leave the company or not. In CC, Hollander actually can't fix what is wrong with Genesis. In the Borne Legacy, the scientist can fix what is wrong with the super-soldier. Even with that change though, once Genesis does get fixed by the Planet, both CC and the Borne Legacy end in more or less the same place. The super-soldier goes into hiding from the organization they once worked for... and gets away with it. The one major difference between CC and The Born Legacy is the attitude they take towards how "right" the super-soldier was in trying to leave the organization who experimented on him. In CC, it's almost always treated as being what the character shouldn't have done and the whole game focuses on how Genesis leaving caused tons of problems for everyone else in the organization. In The Borne Legacy, it's treated as being very understandable even though a lot of people in the organization end up dying as a result.
If I had to say what Genesis reminds me of in Western tropes and not JP tropes... he'd be that really passionate literature/mythology professor who is obsessed with finding that one missing part of a work/play/myth cycle... who just so happens to be one of the top-ranked fighters at the local martial-arts club... and the other two guys at his level are all crazy strong ex-military guys. Like... Genesis makes me think of what Indiana Jones would be like if he went into the military instead of archeology.
There's a definite feeling in Genesis's character that he really shouldn't be in SOLDIER, but should be like... researching old Ancient texts off in some university somewhere (Genesis would fit it at Cosmo Canyon amazingly well). Only as far as I can tell, there is no universities in FF7, at least not for stuff like historical research. Instead, there's Sephiroth, the poster-boy for Shin-Ra, advertising about SOLDIER. And Genesis really wants to get out of Banora...