It takes a while to work up the best load, sights, and individual combination with a good Sharps repro, but they can be surprisingly accurate.
When I worked extensively with a Ruger No 1 in .45-70 years ago, I was able to put 3 holes under an inch at 100 yards using smokeless powder and a relatively inexpensive sight setup.
Dedcicated BP shooters with a good quality Sharps repro may spend months trying different load combinations to get the right one, and with a GOOD (as in expensive) set of sights I'd see an inch at 200 yards as being far from impossible.
The people at Ballard tell me they don't even start to measure accuracy on their big-bore single-shot rifles till 200 yards & say the bullet doesn't "go to sleep" (stabilize) till it's beyond 100.
As far as "all of" the repros goes, I wouldn't make such a broad statement.
My Shiloh Sharps could be right in there, with my load, IF I bothered with long-range sights. Since it's a 100-150-yard rifle, I stay with what I have.
And, it can be quite accurate at 100 yards with a heavy 520-grain lead bullet I cast myself. Have not tried it out to 200.
Denis