I doubt that the Mitzvah of Hashavas Aveida would mandate a person to check items on the “Hefker Table” for Simanim, laudable as the practice may be.
Certainly, everybody agrees that the best case scenario is to have the item returned to its erstwhile owner.
Practically speaking, however, Shuls and the like can not afford to hold on to all of the lost and forgotten items in their premises. This is the reason for the policy of declaring the items Hefker.
These are items which have been left by the owner for a sufficient amount of time that the Poskim have determined that the owner may be assumed to have been ?????. As such, the finder is technically permitted to keep the item, even if he knows who lost it (although in most cases he should return it, as is mentioned in Shulchan Aruch). I would think that the Inyan of Lifnim M’shuras Hadin doesn’t require me to search for a Siman on something which I have not yet picked up.
BMG semi-annually holds a sale of all the Seforim which have been left in their lost and found (I don’t know if they sell everything, or only those Seforim that have been there for at least a year or some other set time). Any Sefer found to have a name may be taken for free in order to be returned to its former owner.