The problem they are up against is that Apple doesn't let you cherry-pick specific devices to support or not support, you have to select from a matrix of features and iOS/ARM versions. So if they want to support the iPhone 5 for example, they also have to support the much less capable 4S.
Bringing in the original Mini would require support for all other iPads except the original iPad. These devices simply can't handle the features of the app. I'm not sure how useful it would be to support these less capable devices if it required dropping video streaming for example...