It’s the difference between the requirements for editing, and the much simpler requirements for final delivery.
In editing, you need maximum flexibility, overhead, resolution, and margins to make changes, whether that’s redistributing the tones, preserving highly saturated colors, or making local adjustments. 16 bits per channel (and similarly, the full original color gamut), gives you the resolution and room to maintain quality as you make change after change. The tonal resolution of 16bpc helps prevent the banding that large changes might create.
But when you are done with changes, it is much less necessary to preserve all of the overhead. You can just keep the final results, and drop much of the rest. The copy sent to a print shop can be flattened, 8bpc, and even JPEG (if high quality), and the final print will look good, because the penalties for stepping down the specs don’t happen if the print shop makes no further major changes to that file.
Another reason is that a print can only reproduce a smaller dynamic range and color gamut compared to the original file and on-screen editing, so print can’t reproduce it all anyway. What can be reproduced in print is typically reproducible at 8bpc, again if no additional major edits will be made.
This works the same way with the digital music and movies you enjoy. The digital files that you listen to or watch sound and look great. But the rendered digital files delivered at the movie theater or on your home AV system do not match the file size, bit depth, and quality level of the original media files (stacks of tracks and clips) that were put together to create the final movie or song.
We even know this with food. What we eat is a plate of food, and that’s exactly what we expect. But the meal could not have been prepared only with the plate and the space on it. Preparing the meal properly actually requires a much larger work surface, more ingredients (like it needed half an onion, but the store will only sell you a whole one), and a lot of water, energy, and a range of tools. But delivering the meal no longer requires all that overhead, all we need at the table is that one plate with the finished dish on it, that will not be altered any further (except maybe with a little salt and pepper).