it wasn't till Girls Band Cry that I even thought about CGI

That's also what made me sit and really think about "why does this look so bad" and try to analyze it fairly. Because it did have style to it, and some of the shots were actually pretty good, but it still just looked bad aesthetically, albeit better than CGI generally does. The biggest thing for me was the backgrounds, though: instead of static scenes that imply motion they had these super busy and cluttered scenes where everything is in motion and there are tons of background models doing generic walk cycles or something and it just doesn't work, it breaks this economy of motion and detail that should be keeping all the focus on the important parts of the scene. The smooth motion also just didn't mesh with the stereotypical anime overacting conventions - I think this is the same thing you're saying looked like they were puppets and I can see that, since it does look like the sorts of motions that would be used to convey emotions and actions with the limited range of a puppet.