I recently came across the reference in Theodor Birt that reminded me of an old problem. After a description of the production of papyrus sheets, Birt states that “the resulting sheets were sold individually (Die so entstandenen Blätter kamen einzeln zum Verkauf)” (Birt, Die Buchrolle in der Kunst, 1907, p. 6). The common view now is that the unit of sale for papyrus was the roll and not the individual sheet. The fact that we find kollēseis (the overlap where sheets are joined together) in the bifolia used to make up papyrus codices would seem to be decisive evidence that papyrus was purchased in rolls rather than individual sheets, at least in the Roman period. In some cases, we can even reconstruct the rolls from which the bifolia of papyrus codices were cut (scroll down at the link here). And we also find kollēseis in documentary letters, which suggests that these too were cut from rolls. P.Oxy. 42 3057 is a nice example of this phenomenon. It’s a letter (likely of the first or second century CE) with a prominent kollēsis running down the right side of the papyrus.

It’s certainly understandable that views change over time as new evidence accumulates, but there are a couple things about this quote from Birt that give me pause. First, no reference is given. Birt knew the literary and iconographic evidence very well, and he regularly cites his sources. It’s odd that he does not do so here, and I wonder what he may have had in mind. Second, I had thought one explanation could be that Birt believed, as many scholars did in those days, that the word χάρτης (Latinized charta) generally meant “sheet of papyrus” rather than “roll of papyrus” (the latter is the consensus view today). But now I see that Birt quite clearly regarded χάρτης as “roll” already in the early twentieth century. In another book, he wrote as follows: “In order to describe a roll as a roll per se, the Greeks used the words βύβλος, βυβλίον (or βίβλος, βιβλίον), χάρτης, χαρτίον (Um die Rolle als Rolle zu bezeichnen, …etc.)” (Birt, Kritik und Hermeneutik nebst Abriss des antiken Buchwesens, 1913, p. 274). So, I am still at a loss as to Birt’s source for the idea that papyrus was sold by the single sheet rather than the roll.
But this brings me to a second problem less directly related to Birt. As I noted above, it’s clear that most papyrus codices were made up of bifolia cut from rolls. The presence of kolleseis demonstrates this point, as does the occasional appearance of the prōtokollon among the leaves of codices (the prōtokollon is the first sheet of a roll, with fibers oriented at a 90 degree angle relative to the fibers of the rest of the roll).
What bothers me is that, when you are trying to make a papyrus codex, working with papyrus that has been rolled up is really challenging. The tendency of modern papyrus to curl is very strong. Even papyrus that is shipped flat tends to curl when not kept in a folder under some kind of pressure. I usually steam sheets and dry them under heavy weight before I arrange them into quires. This is a time-consuming and somewhat awkward process.
I’m aware that commercially available papyrus is not made in the same way as ancient papyrus. The modern process involves the use of chemicals and alterations of the color (there is an excellent video about the modern production process in Egypt that you can watch here). Ancient papyrus tends to be much finer (thinner) than modern attempts, and may well have had other different physical properties as well. But I wonder if the makers of ancient codices also encountered these kinds of problems, and if there were sources for buying papyrus by the sheet. Some papyrus codices, namely the Manichaean codices from Medinet Madi, are occasionally said to have been produced from specially prepared sheets and not from rolls, though it’s hard to be sure about this (only clear differences in fiber patterns across all bifolia or the complete absence of kollēseis would be compelling evidence, and these codices are too poorly preserved to make those type of judgements).
Finally, I should close with James Robinson’s observation that many of the Nag Hammadi codices (probably produced in the mid-to-late fourth century) seem to have been manufactured from rolls that were made up of very long kollēmata (sheets well over 1 meter long, as opposed to rolls with shorter kollēmata of about 20-30 cm in the preceding centuries). So by the fourth century, the method of manufacturing papyrus sheets seems to have changed, such that entire height of the papyrus reed was used to make large sheets. But even these, it seems, were still pasted into rolls to be sold and used by codex makers and others.
I am not a papyrologist, but brief consideration and brief search (maybe nothing definitive) leads me to speculate that at least some flat papyrus sheets were made available for use before being joined into long rolls. Why not?
I have no objection to the idea of the sale of single sheets in antiquity in principle. I’m just wondering what (if any) evidence Birt used to make his positive claim that it was the norm.
Your perceptive observation that Birt, anomalously for him, did not cite a written source suggests he did not have one. Possibilities include that he may have seen modern sheets for sale, and retrojected that. I haven’t read his autobiography, Wie ich lernte (1929). Or he may have guessed that if a buyer wanted a sheet, a seller would provide such. Neither would explain nor justify the either/or, sheet/roll, matter. But it may lead to a question: how hard was it to join sheets? Say, a non-professional wanted to replace a protokollon, or any two pieces. Would that typically be sent to a shop or be a do it yourself job?