I know your question was probably rhetorical but there actually is a reason why Broadway is relying on reality shows now. Unfortunately, like everything else, theatre is a business. Although it provides enjoyment (and employment!) to a great many people, it exists primarily to turn a profit. Broadway has changed a lot over the past few decades. In the 1950s, for example, some of the biggest stars in the world were created on the Broadway stage (e.g. Ethel Merman, Mary Martin, etc.) but now most of Broadway's well-known names are huge stars in NY and no names elsewhere (e.g. Sutton Foster, Idina Menzel, etc.). Broadway has also become more of a tourist-driven industry. The shows that bring in the out-of-towners are either the huge well-known hits or things with stars in them. With the industry as fickle as it is now, not as much time is given to shows that have the chance to become word of mouth hits if given the chance to get its name out there and spread some good buzz. Reality shows are popular on TV because they are extremely cheap to produce and bring in good ratings - a network exec's dream! They are also shown on a national scale so viewers everywhere get a chance to have their say. Tourists who may have voted for Max and/or Laura on the "Grease" show can say they saw them on TV and now want the chance to see them live. It will probably be the same with whomever wins the "Legally Blonde" search.
For me personally, the problem with the reality show casting isn't the concept but rather the execution. Some of the girls on "Legally Blonde" have professional credits and would possibly be in the running at a cattle call audition anyway. My problem with the shows is that I think the level of talent is subpar and the production values are terrible. On "Legally Blonde" for instance, the last thing you need in a high stress environment like a Broadway audition is to live in the same house as your competitors. Reality shows featuring all girls generally show off the absolute worst female stereotypes - the backstabbing and the gossiping. "Top Model" is the same way. They are all living together just for the drama.