Currently saves searches can only be shared with your current IPK/ Workflow group in ASM which limits the ability to share searches out of the box. It also means if someone shares a search the people in their group have no choice but to have it in their saved searches.
It would be better to be able to allow people to share their saved search (tick the box) but not allow people to choose a group to share it to but allow other people to go to a screen showing all shared searches (which include info about the search e.g. name of it and who created it) and allow people to add them to their saved searches where they feel necessary. This would add flexibility to sharing saved searches and make it a better experience to analysts too.