I won't argue your other points, but regarding Raku becoming the head of the Yakuza... I think it makes sense that he has become more willing to lead the group.

For the first 160-170 chapters of the story (or up until the point he started to fall in love with Chitoge), Raku was absolutely devoted to living a peaceful life without any disturbances. He wasn't willing to leap out of his comfort zone - and this was one of the reasons why he refused to acknowledge his feelings for Chitoge early on and why he hung onto his crush on Onodera for so long.

Raku longed for a life that could be easily calculated and a partner that was predictable, calm and well-within his boundaries of comfort. For someone as peaceful as Raku, somebody like Chitoge was a lot for him to handle at first. Chitoge was (and still is) extremely explosive, unpredictable and overall the opposite of Raku has been used to all of his life. For him, he was too scared to step out of this comfort zone until Chitoge gradually pulled him further and further away from the things he was used to. Somewhere down the line, Raku began to appreciate all the attributes Chitoge had - no matter how uncalculated and inexplicable they were.

Basically, what I'm trying to get at is that at the beginning of the story, Raku didn't want to stray away from a life he was used to. However, when Chitoge came along and showed Raku a world he wouldn't dare step into alone, this promoted a change within him. Now, he is able to accept the Yakuza, even if it brings him a life full of unexpected and crazy things.

Similar to how he has come to accept Chitoge.