Yes. It is possible to delete a custom profile other than the Guest Profile and Shared Device profile. Deleting a child’s profile will move all devices in it to the Unfiltered Devices list and not get any filtering rules. Any school-owned devices in the deleted profile will continue to be filtered as per the take-home policy or off-site policy determined by the school.
To delete a profile navigate to the "Child Profiles" tab on the homepage and select the profile you wish to delete. Next tap the "Delete this profile" option to delete it permanently.
Alternatively, you can also go inside the custom profile you want to delete and tap 'Delete this profile' option.