This actually should work, but getting drag/drop right on iOS devices is hard. They just don't have the CPU to rerender our sticker dragging fast enough to make it feel like you're dragging a sticker; you tap and drag and it never catches up to render so you never see it work.
We'll optimize the mobile experience and devices will get better, so the HTML version will be good enough at some point. In the meantime we will, at some point, invest in mobile Canvas apps (Android and iOS).