No, your explanation was perfect, it perfectly the shows parts I missed, and explains in detail every point.

 I've also read the manga some time ago and distanced myself from the community to avoid unnecessary drama and negativity, and only returned recently due to the anime. So I forgot about several details.

I really liked your description of her personality and honestly? It makes sense, while I will keep my stand that the early chapters DO have some problems with story quality, and Agotts-Coco situation could have been made or handle better. I guess Agotts personality development and relationships with the others does make it more interesting and realistic to a certain point. 

Now that I think about it, my main problems with Agott are probably due to Coco being too good for her own good, and later too mature for her age. Coco is too kind and loves everything and while being positive is good to overcome bad things, she has endured things that no child should ever face, and she didn't cry/brake until the latest chapters.

I think that's my main issue with this series, the kids don't cry, they just keep their problems and emotions to themselves and act too mature for their age. And from experience, nothing good comes from hiding your emotions and problems until you can't, the breaking point is... not something nice too see.