You can also just reach out and flick the page on the touch screen, not as elegant but more predictable than flipping a printed page -- at least your sheets won't go flying. Managing page turns does get easier with experience, and you learn to prepare your charts -- taping them together, dog-earing them so you can quickly grab a corner, sometimes cutting things apart and rearranging so a page turn happens at a convenient location such as a couple measures of rest.
I'm a jazz musician, and have a Windows tablet, that was a hand-me-down. It only has a 10" screen, making conventional music notation hard to read. It's OK for reading chord symbols. I also have a notebook PC with 14" touch screen, that can operate in tablet mode, so I can lay it open on my music stand. That's a lot more readable, and has full blown computer functionality if I need it, but of course there's the danger of the stand tipping over.
Admittedly I still prefer paper, for one thing it's a lot easier to annotate with a pencil, quickly.
100% of my colleagues are using ForScore on an iPad for these purposes.
Great feature set, great support, stable, very fast. And page-turning is ultra-fast. If you need that to be hands-free, there are numerous hardware options for that.