I use a variety of sharpening mediums depending on what I am sharpening and my mood. Abrasive paper on a flat backer is certainly an option. One drawback of using abrasive paper is the fact that you have to be very careful if you push the blade forward to keep it from digging into and cutting the paper. If you sharpen freehand you can skew the blades if your stones are only slightly less wide than the blades. I normally reshape blades on an electric grinder (when necessary) and stone them on diamond plates which don’t require flattening. I do sometimes use oil stones and a ceramic stone which I will occasionally flatten with a diamond plate and/or abrasive paper on a surface plate. I don’t have a lot of experience with water stones but was put off by the mess of water/swarth and the near constant need for flattening. I tried ending by polishing with a 16,000 grit ceramic stone but found I can achieve a superior edge by simply going from a 1200 grit stone (or paper) to a hone/strop to remove any wire edge and give the final polish. Any rounding of the edge is negligible compared to the benefits of the highly polished surfaces and edge. For those on a tight budget, abrasive paper followed by honing is an excellent short term option. Another advantage of using abrasive papers is that they can be wrapped around convex surfaces for use for concave bevels for things like curved spoke shaves, molding planes, and in-cannel gouges.