It's hard to tell wether or not you've really looked at ImageMagick. I had completely forgotten about Xv - it must be five or six years since I last used it. I'm using ImageMagick for the kinds of things that I would have used xv for.
Comparing against your criteria:
The ability to quickly step through a set of images, preferably with an easy keystroke (such as the space bar).
ImageMagick can do this with the "display" program. "display *.png" or whatever. Space to go forwards. Backspace to go back. Completely clean interface with no superfluous controls - unless you click on the image. Very nice.
Display of images in their natural resolution whenever possible.
Yes. Nice panning feature if the image is too big for the screen.
Fast operations for cropping and resizing images, and for saving the result.
Yes. A few mouse clicks. Could be faster as there is no toolbox - so the menu has to be navigated. But not really a big problem. The big plus with ImageMagick is that you can also do all these things on the command line.
The ability to take a screenshot of another application is a nice bonus.
Yes. With the "import" command.
Also nice, but less important, is the sort of quick color table tweaking that xv supports.
Yes. With some caveats. I don't do much of this so can't really compare with how xv does it. But you can fiddle with contrast, hue etc. Various effects and so forth. "man display" gives a pretty good idea of the feature set.
I find it surprising that ImagicMagick isn't the complete replacement - you don't really say why it doesn't do what you want it to do - which makes me think you are missing out on something.
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