All true, but the main point is that the subject of BBT isn't "geeks", which explains the misguided haterade. For example, Raj seeking research/grant funding from Sheldon and their university office sharing hijinx hits home for a segment of nerds who aren't the type to frequent reddit or HN where the "laugh at geeks" narrative became popular.
This is esp. cogent if Community is supposed to be a "proper" nerdy show. The reality is a single-camera format is more conducive to a more subtle script (eg 30 rock, which geeks similarly like) than a cheap/quick multi-cam sitcom. The love seems to stem from the nature of the material, which is conflated with the material itself.