I totally agree with that - a very common usage will be to look up a login … right now you have to manually type the search icon, wait for the search window come up, type into the search box …
This is unusual behaviour - usually you have the search box right at the top of any list, compare all iOS default apps / lists like in contacts or iOS settings …
As mentioned KeePass Touch does it nicely …
This is my number one change request … thanks.