According to Stein Erik Skar's book The Concert Years about 50 hours were filmed from Elvis' concerts, the record studio and from the activity surrounding the concerts. Given the wealth of material filmmakers Pierre Adidge/Robert Abel had to work with, I think they did a good job editing the film.
That said, a special edition could, of course, be even better. The question is how to go about it. One approach could be a complete re-edit, to make it into a That's The Way It Is-movie, that is, let it start with the mock session/rehearsals recordings and then continue with the live performances. But maybe that's a questionable solution, as it would certainly go against the original intentions of the producers.
Another, and maybe more acceptable way to do it, would be to keep the original plot, but add new material and in some cases also delete some things. One example of the latter that immediately comes to mind is the scene where a very old guy wearing a hat, in a weak voice tells us which doors Elvis is going to pass through on his way to somewhere. Boring stuff.
More exciting is the prospect of adding rolls of films. The fantastic version of "Always On My Mind" from the mock session is a given. Also, I would like to see some more material from the rehearsal recordings, such as "Burning Love." In the original movie only the religious material from that day is used, to illustrate Elvis love for gospel music.
And of course, the addition of more live performances, is what really would make a special edition special. Immediately missing songs such as "How Great Thou Art," "I Can't Stop Loving You," "Release Me" and the incredible version of "Are You Lonesome Tonight" from Elvis: The Lost Performances comes to mind. And complete versions of "Suspicious Minds" and "Until It's Time For You To Go."
One thing I haven't made up my mind about is whether to keep the scenes from the 50's, including Elvis' performances on the Ed Sullivan Show in 1956. What do you think?
PS: While I wrote this I listened to Live In Texas 1972, the final CD on the Close Up box set released in 2003. It features the next to last concert Elvis did during his April 1972 tour, in San Antonio. What hit me was that none of the older songs done in that breatless speed ("All Shook Up" and "Teddy Bear"/"Don't Be Cruel"among them) were included in Elvis On Tour. A wise choice.