Some shows really do benefit better from this than others. I feel some of this season's shows like WEST SIDE STORY, SHREK, STORY OF MY LIFE, etc lend themselves better to studio recordings. The most obvious choice for a live recording this season is HAIR, and after listening to the wonderful recording, I still feel it lacks a lot of the energy that just comes from performing the show live (and I don't mean for this recording specifically, I never liked HAIR on recording--except for a few songs--until I saw the show live and finally "got" it).
There are some where I don't think it makes much difference, the PASSION London recording was recorded from a concert version that reunited the principals. I don't see much of a difference in terms of how the overall recording comes across (I suspect Maria Friedman's Fosca would have been as misconceived on a studio as it was on stage).
"Some people can thrive and bloom living life in a living room, that's perfect for some people of one hundred and five. But I at least gotta try, when I think of all the sights that I gotta see, all the places I gotta play, all the things that I gotta be at"