Print scans are kind of an existence proof that there is a real print somewhere in the world, but I wouldn't assume that a scan of a print necessarily looks more like the print than a negative scan adjusted to look like the print. They both take a fair amount of work, in my opinion, to go from the raw scan to an image on the web. Ultimately, there is no way that an image on an illuminated screen will ever look like a print on paper, so it's all illusion anyway, and is it more important to know that a print exists or to see an image that looks like the print? If you want to see prints, then participate in the print exchanges and traveling portfolio, and that will be way better than any kind of digitized image.
When I was using a flatbed scanner, I usually found the artifacts from print scans to be problematic enough that I preferred to scan negs and adjust them with the print in hand, and that I could get a screen image that looked more like the print from a neg scan than the print scan. Whether scanning artifacts are a problem for you will depend on the paper you use, the scanner, and how flat the print is.
For alt process prints, there really is no option other than scanning the print, because you aren't even going to get close starting with a neg scan. Also, they aren't going to be as glossy as gelatin silver prints, so the surface artifacts that show up in a scan are likely to be artifacts that are actually on the print, rather than scanning artifacts. Obviously, if one wants to show specific print effects like toning, bleaching, or lith printing, it's easiest to scan the print and accept the other sacrifices that come with that.
Part of the reason I gave up scanning for a copy stand and DSLR is that I could control the light, as I could with traditional copy work on film. I also happen to have good lenses for this purpose, so I figured I might as well get some more use out of them.