Saving large stacks with “File - Save as - Zip…” works very well. But, by default, Fiji uses the SCIFIO image file opener which takes so long to open a zipped file that the user thinks it failed to do so.
It is unfortunate that SCIFIO is enabled by default. To disable it, go to “Edit - Options - ImageJ2…” and untick the checkbox for SCIFIO. (It reads “Use SCIFIO when opening files (BETA!)”).
With SCIFIO disabled, .zip files will be opened fast, when large it will feel as fast as non-zipped files.
This issue has existed for years, and remains a relevant issue for anyone dealing with large collections of image stacks, that is, almost all biologists.