Image Capture "Delete After Import" Disappeared
If Image Capture detects that the device uses iCloud Photo Library, it disables 'delete after import'.

You can tell when the program starts the option shows, then a split second later, when the iCloud icon shows up next to the device, the 'delete after import' option is gone.

Here are some work-arounds:

On your device, go to Settings > iCloud > Photos > and then turn off iCloud Photo Library. This of course has larger repercussions (photos are no longer saved in the cloud).

In Image Capture, with your device connected, select all the photos you want to delete and then ⌘-Delete