Why choose anything but highest compression for PNG? I just installed LibreOffice for the first time. In the Impress
application for presentation slides, when I choose to save an image on
a slide, the file type is PNG and there is a slider for compression,
positioned approximately midway at 6. Internet searching reveals that
PNG compression is nonlossy.  Why would anyone choose anything but the
highest compression?
Simply because the highest compression typically is significantly more CPU-intense (it tries out multiple different approaches to represent successive lines).

This really shouldn't make much difference on a modern PC for saving a few images. Then again, in practice, libpng seems to be pretty slow, so this might make a difference, especially for people working on older devices.