Make no mistake, Denver was added to the Big East not because there was some long-term hope of them being added as a full-member, but rather because there was a mutual benefit to both parties in the name of lacrosse.

The Big East began sponsoring men's lacrosse in 2010. Georgetown, Notre Dame, Providence, Rutgers, St. John's, Syracuse, and Villanova all participated. When realignment occurred, Georgetown, Providence, St. John's, and Villanova became members of the reconfigured Big East. Marquette, which announced plans to add the sport for the 2014 season, also joined. Notre Dame and Syracuse joined the ACC, which already sponsored the sport. Rutgers spent the 2014 season in The American before joining the Big Ten. Since Rutgers was the only current or future full member of The American that sponsored men's lacrosse, it remained in Big East lacrosse until the Big Ten began lacrosse competition through 2015.

The ECAC Lacrosse League was a national lacrosse-only conference which had included Georgetown, St. John's, Rutgers and Denver. Needing members, and having a former association and relationship, Denver (with its private status) was a natural fit.

On the women's side, there was a lot of membership changes going back to the early 2000's, and especially with the BE/AAC split. The split left the Big East and The American with too few lacrosse teams for an automatic NCAA bid. The Big East was the league to sponsor women's lacrosse (until 2018, when the AAC began to sponsor it as well, taking its associate members away from the BE). Women's lacrosse will have seven members, with the return of UConn, this summer.

Long-story short - the partnership between the BE and Denver is rooted in lacrosse only, not some larger, grander, long-term plan that could culminate in them eventually becoming a full member. Denver has little-to-no basketball history, little-to-no presence in the NE and has never put forth resources to be competitive in men's basketball (which is totally fine, all athletic departments are different). While there was a fit in lacrosse between both parties, there really is none when it comes to basketball IMO.