FFXIVs item search is more to find which of the many inventory partitions an item is in, rather than the precise location within any of those inventories.
Considering this game has dozens of tiny inventories instead of one big one.

If you need to find something within an inventory, you just... look at that inventory, it's not so big you cant find it by glancing at it for a couple of seconds.
You can sort the inventory to make that easier.