I think it would have to be on a case by case basis. The question I think we should be asking is: Would the database or the website be easier for the "average listener" to use if you made this change?
In the case of Henry Mancini I think it is. Most people aren't thinking of Moon River as a song by "Henry Mancini, His Orchestra and Chorus", they're thinking of it as a "Henry Mancini" song. So now it's on Mancini's discography, making it easier to find, but it's still correctly credited.
An example of a group I don't think would benefit from splitting and using artist credits would be "Simon & Garfunkel". I'd say most people think of the group as separate from its members, and I doubt there's a significant amount of people coming to the website and looking for Sounds of Silence in Paul Simon's discography.
As for Bill Haley, I think a case could be made for splitting and recombining. We have "Bill Haley", "Bill Haley & His Comets", "Bill Haley and the Saddlemen", "Bill Haley & Four Aces of Western Swing", "Bill Haley's Comets", and "Bill Haley's Comets with Joey Rand". Breaking those up into their constituent parts would put all of Haley's work and all the Comets' work in their respective discographies. I could also see this treatment benefiting Elvis Costello & the Attractions, Bob Marley & the Wailers, and Bruce Springsteen & the E Street Band.