It seems like quite a few of the drummers did not want this job more than anything else. "Honored to be asked", "cool to try", "we'll see what happens" seemed to be the vibe. Their level of excitement could've been ascertained through a phone interview, saving Team Dream Theater thousands of dollars in travel & lodging.
Mangini was "one of the first drummers to pop into our heads." For several of the other guys, they found them online in lists of drummers people thought would make good replacements. The whole 7 Drummer audition allowed them to show (and convince) most of their fans that Mangini ruled and various fan favorites, while great, were not as perfect a fit.
I think the audition process, and those asked to audition would've been very different if carried out in private. But this method killed several birds with one stone (help fans accept MP's leaving, promote new drummer, promote new album, show fans they will still give us inside looks, etc.) and would've taken out even more birds if VH1 or MTV had bought it!