I used to have hierarchical inventory management in QuickBooks. In ERPNext only the the first parent Item Group is searchable in item child tables. Also the print format and reports only includes the item code(without the parent group names).
I asked this question some time ago, maybe it will give you some ideas. The docs may also be helpful.
It may also be helpful to say for what purpose and why items should be searchable , and maybe also by who. The Report Builder capabilities and custom reports can be useful when the standard search methods do not suit one’s needs.