I personally think the whole idea of a 'dvd of shuffled, bad quality songs a band plays at a concert' is not really interesting, and do not remember ever buying a music dvd. Maybe that's because I really like the quality and cohesion that a cd can offer both thematically and musically (which is usually the case for Theocracy, among others), or it's just because I'm being a terrible person here, but to be perfectly honest wouldn't be all that excited about a live dvd. But hey, who am I?
I agree with what you're saying. If I had to pick just one, I'd say studio over live any day.
But some of the advantages of live albums are:
changes to songs after they are recorded that the band wishes were on the album (an extra harmony, different lyrics, etc) that actually are better than the studio version (or with a better line-up, like Dream Theater's live re-recording of their first album but with LaBrie on vocals),
references to their other songs - or other band's songs - during the performance (Symphony X ending a song on the YYZ ending, Dream Theater going into the Freebird solo or Enter Sandman, the ever popular Hallowed Be Thy Name ending that sounds good after just about anything (X-X-X-X, X-X-X-X///), etc). These are nice little surprises that make live albums interesting (I will admit that prog metal bands are probably the best at varying their sets in this manner - many bands play the same songs the same way at every show for their whole career...that IS boring),
creative flowing setlists where many of the songs have transitions between them - songs that aren't from the same album but that sound great together in the set,
extra solos (Paris Is Burning), extended intros (live intro to Xanadu or The Killing Hand) and outros,
hearing and seeing a little bit more of the band's personalities and the way they interact with each other live (G3, Iron Maiden, very visual live shows like Rush, Matt Smith's very metal frontman hand movements and facial expressions that go with the lyrics (a la Bruce Dickinson)),
and there are several other things but I guess I've made my point. I'm just saying that live albums do have their place, but I will agree that the quality of studio is better - being able to have complete control and take the time to get it perfect. But I also think live albums
can be very cohesive depending on how they're done. I would rather listen to Dream Theater's Metropolis Part 2 live than the studio version (a rare instance of that for me). The Metropolis 2000 live DVD has a huge, thick sound and I think the studio version sounds a little thin next to it, but that's just my opinion about that one album.