I've mixed a bunch of live Gospel Albums while watching the video playback, which, I THINK were usually the final edited versions, or from feeds that were switched live, without any ISO cams, to the "Master" video.
I've done a lot of them, and I can't be certain which ones were which, since the budgets are usually very small, and the mixes are done so quickly, but MOST WERE final video edits, and I mixed to those.
When I DID know it was the 'Final Cut' video, no matter if they were switched live, or ISO edited picture, the fun part was always kicking up the instrument seen on cam a dB, or so, to sync with the video, as corny as that seems.
The only real drag was the "Chase" and "Lock Up" times, when doing things totally linear, using tape, (audio and/or video, no hard disc stuff used), especailly when dealing with any console automation trims, updates, etc....
BUT, I'm an Analogue guy at heart, so it's all good!!
I've also done live mixes to broadcast, straight from the console to "Air", with a multi (24) track, and the stereo audio on the video deck as backup/archive, which is REALLY fun and challanging!!
A fixed wide shot is REAL helpful, especially if you've never heard or seen the band before, but I usually would get the 'On Air' feed, and just be playing the console, like I used to mix 'Records', in the *Good Old Days*!!