I did take that into account, but didn't have time to research WCHA league membership all the way back to 1948, sorry. Michigan has won nine titles, how many as a WCHA representative, I have no idea. MSU has won two, in '66 and '86. In '86, at least, they were members of the CCHA.
The point was more about HE's lack of titles.
Read the sentence above as it applies to WCHA teams, the same would apply to teams from all other conferences.
The point remains, in the grand scheme of things, HE has not had much success winning ice hockey championships.