Paper patching is fiddly, no doubt. As you mentioned, the old guns with Henry style rifling or the shallow Sharps style may benefit from using the paper patch as that was what they were designed around. One other advantage is that at higher velocities the paper jacket allows a softer alloy to be used for hunting - at least that is the concept I am investigating.I rolled a few with my 45-90, seemed more trouble that it was worth it for my rifles.
In BPCR I have the three Browning rifles.
40-65 45-70 and 45-90 Creedmoor, I swapped out the factory sights for LR MVA Buffalo's.
Fun fun stuff to shoot.
If I had a vintage Sharps or a Rolling Block I definitely would spend time with paper patching.