In my previous posts about making a model of Beatty-Michigan codex of the Pauline epistles (P46, TM 61855), I discussed the sizes of the bifolia and the curious fact that P46 seems to lack any evidence for the presence of protective parchment or leather stays in the center of the quire. Another issue related to the absence of evidence for stays is a similar lack of evidence for the presence of a spine lining strip or a cover. Just as the stays prevent the binding thread or tacket from ripping the papyrus leaves at the center of the quire, the spine strip protects the outermost bifolia from the binding agent, and the cover protects the whole codex.
Several of the Nag Hammadi codices have well preserved leather spine strips that are now kept together with the covers. Here is the cover of Nag Hammadi Codex IX (TM 107749). Notice the papyrus scraps that still adhere to the spine strip.

A spine strip also appears to have been preserved with the Crosby-Schøyen Codex (TM 107771), The darker leather is just visible along the spine in this photograph of the codex before it was disassembled:

In the case of P46, the absence of evidence for a cover and spine strip is understandable, since the outermost bifolia of P46 did not survive. So, even though there is no surviving evidence for either a spine lining strip or a cover, it seems reasonable to expect that they existed. Based on that reasoning (plus the practical point that threads cut right through the papyrus without a spine strip), I added a leather spine strip to the model I made.

I decided not to put a cover on this model, but I am pretty firmly convinced that P46 and indeed most papyrus codices, probably had covers. I recall reading somewhere (I can’t come up with the exact reference) that perhaps the presence of covers on papyrus codices was exceptional. I find this a bit difficult to believe for a couple reasons.
First, papyrus codices, especially single quire codices, tend not to stay closed. There is a snake weight in this image above to hold the codex shut because what it “wants” to do is spring open. A cover with a flap and ties keeps the codex codex closed.
Second, papyrus leaves do not do well without some form of protection. This quire endured just a few trips between office and house in my backpack, and it already has begun to show signs of wear at the edges.
Papyrus books with leather covers, however, are surprisingly durable. The model I made of Nag Hammadi Codex VI can be shaken around by the cover and generally abused without showing any significant damage. I think this kind of cover must have been the norm for papyrus codices in antiquity.