I thought I downloaded a bad .dmg file. But no, after two more from two different other developers, including a re-download of a previously mountable one, now I can safely conclude it's the abomination known as DiskImageMounter and its henchman diskimages-helper that are the real culprit for this latest string of supposedly unmountable images. I'm sure nothing short of a reboot would fix it, unless I want to bother figuring out which launchd job or two I could give a kick to.
I think what triggered this is simply downloading a few .dmg files and trying to mount all of them via double-clicking in quick succession.
Based on what I've read about DiskUtility in 10.12/10.13 and iOS 11 in other threads, I can imagine things could be only getting worse in later OS X.

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Once the download is complete, you will see a file with the extension '.iso' or '.dmg' in the download directory. Open the downloaded.iso/.dmg file with the Disk Image Mounter utility, which is installed on all Mac OS X computers. Gparted live usb ubuntu. Right-click the file and select Open with DiskImageMounter from the menu.