It seems, as if the procedure of an OP is not known to us sufficiently enough to analyse the tagging of the instruments with RFID tags. I do not know it either, so I asked a physician and a nurse and here are the most interresting findings in no special order (valid in Germany, but I don't think that these procedures differ a lot in world).

- the number of instruments used is not known beforehand.
Simplest reason: the surgeon dropped the last scalpel on the floor and needs a new one, but there are a lot of other reasons like the need for another size or similar. There is even a special nurse for such incidents who passes instruments between septic (e.g. storeroom) and aseptic (the OP-room) areas.

- instruments may break in pieces.
Obviously only one of these pieces has the tag.

- some instruments are very small and cannot hold a tag, e.g. a needle.

- it might be difficult to tag something like a swab.
A swab is probably the most forgotten surgical equipment.

And with this in mind and knowing a bit about the RFID technique I cannot see much use for tagging surgical instruments in parts beside easier storage- and desinfection managment for the patient but the advantage of have no false positives if the patient itself is "wanded" (is there no word for "checking for a RFID-tag with this curious thingamabob"?): if the "wand" detects an RFID tag in the body, there is an RFID-tag in the body.
If you check the equipment for completeness, you'll get at most a complete inventory of all the RFID-tags and nothing more (things may break, some things are not tagged at all, and so on): false positives are possible (there is equipment left in the body despite the correct number of RFID-tags detected). A nurse would see if instruments are broken, would know which equipment is not tagged and handcount them, and so on.

All implementations of such a technique would need a lot of approvement stamps which makes it significantly more expensive.

It's very easy to wave the "wand" over the patient to detect a left RFID if it is detectable (no false positives, but, depending on the kind of RFID technique a lot of false negatives). A RFID-chip has some metal build in and is, depending on the size quite easily detectable with x-ray (some materials are not or at least badly visible with medical x-ray) if some equipment is missed.

So, it has some significant advantages for the patient and might be cheap enough to get implemented if somebody finds a good argument for the hospital because "good for the patient" is not sufficient. Ah, "it makes stealing more difficult" might be a good argument if nobody asks for an actual measurement of "more difficult".