I have the opposite problem, well, my partner does. Her phone regularly fills up completely with pictures so I want to copy them to a server and then delete them from the phone, but for some reason this doesn't seem to be supported. My theory is Apple wants you to keep buying newer phones with exorbitantly priced storage upgrades.
This was a few years ago, and was one of several "iOS breaks our crucial workflows" problems that motivated switching our last device over to Android, so the situation might be better now...but I've never had that problem with the Android client, so I know it's not an Immich problem.