I know BBs very rarely read this thread, but give it a try anyway....
IMHO there are 3 important data about the users team you can not access through BBApi at the moment. Some of them were already mentioned by others, I'll just repeat it:
1., Enthusiasm: Could be available in boxscore or teaminfo, only for the current user of course.
2., Fan survey: Could be in teaminfo or have a dedicated xml, current user only.
3., Number of season ticket holders: As seen on economy page, in economy.xml.
At least I would like to get an answer like "Not possible" or something...