Most demonstrations of old printing presses are of one person hand operating a single press - painstakingly arranging type, inking, rolling, pressing and then drying one measly document. One could imagine this working well for a weekly flyer or newspaper, but how did this process scale up logistically to produce many copies of many books? If a book was 200 pages long, was page 1 set and pressed thousands of times, then page 2, and so on? Or did publishing houses have many people operating many Gutenberg style presses? Could larger presses press many pages at once? All options are still better than transcribing, I suppose!
Given that the European printing machines did not really change much throughout the first 400 years of their existence, i.e. since early 15th century to the very end of the 18th century, as they were almost universally a screw-operated flat-bed presses retaining most design traits typical for the earliest specimens. Thus, the term 'pre-industrial' used below should be understood as a reference to the period predating so-called Second Industrial Revolution i.e. time prior to 1840s rather than the first wave of industrialization in Western Europe that is usually associated with the second half of the 18th century.
First and foremost, as you correctly noticed, the modern reconstructions are usually done for the education and entertainment purposes and not are not meant to be economically viable. In real printing shops, each machine has been operated by a crew of printers to facilitate smooth work. Please note that while typesetter i.e. a person tasked with actual setting the movable types into lines of texts and then into the entire pages, needed to be not only literate but very proficient at reading, the people operating the press did not, as their work was purely menial one. I'm not saying that they were illiterate, as the literacy rate among the craftsmen was quite substantial even in the late Middle Ages, when the printing press gained popularity, I'm just pointing out that the operation involved people of different skills. In most cases, judging from the contemporary accounts, a commercial workshop could employ at least two or three people to operate the press, with typesetters being an almost separate profession and the folding being conducted by students and apprentices at the binding shop that could have been a completely separate facility.
Thus, with a team of printers it was possible to achieve quite substantial output rates. Although Wolf suggests that the capacity of the simple flat-bed printing machine could have reached even 3600 individual prints during the 15-hour work day, it seems hardly possible, as it would require making a single print every 15 seconds without any pause. Given somewhat labour-intensive character of the operation of the manual presses, it is, of course, is humanly possible, but seems highly improbable of being anywhere close to average. A lower estimate of 1200-1600 prints in the same period, yielding a print every 45 seconds (or a bit less) is much more believable, given the necessity to make breaks to rest, replenish supply of ink and paper, do necessary adjustments in the machine itself (inspection, lubrication, tightening), especially if it was old or heavily used etc.
Now, please note that large pre-industrial printing devices were universally flatbed machines, i.e. ones where the frame with the negative of the printed text set in was lying flat and had individual sheets of paper placed in it and then pressed from above to make an even print. To produce a single imprint, the printers needed to cover the text matrix with a thin layer of the printing ink, put a sheet paper over it, slide the entire bed under the press, then press the paper from above with the screw-operated wooden platen, raise the platen, slide the bed from below the press and peel the paper off. Given the adsorption of the paper and the small amount of the paint, it usually dried before the subsequent sheet has been placed on to of it.
Please also note that the books were by no means printed page by page. Depending on the size of the final book, from two to sixteen pages were printed with a single movement of the press. Given that many of the early printing presses were able to print in folio format, i.e. accommodate sheets of paper 24" x 18" or of similar size, it meant that in case of a quite common octavo-sized books (6" x 9") each of such sheets could have been folded thrice before binding. This, as the name of the size suggests, meant that 8 pages of the book were printed on a single side of a sheet, causing the folded sheet (a 'signature' in printing jargon) to consist of 16 subsequent pages of the final book. Thus, a book 240 pages long would consist of 15 such signatures. Assuming the aforementioned speed of 45 seconds per sheet, this gives us 1.5 minute per signature (both sides) and 22.5 minutes per full 240-pages book. In other words, within 12 hours of operation, a single press could produce roughly 25 copies of a 240-pages long octavo book. This is, of course, a theoretical approximation, as signatures were often printed sequentially and while the printers were busy with printing the second one, the first one has been folded, while the typesetters were already preparing the third one. But as one can see, a single large shop using, say, a dozen of printing presses could have easily printed low hundreds of copies each day. Such workshop size also corresponds well to the realities of the late 18th century, when a lot of local printing shops in Poland and Germany were reported to possess between four and fifteen presses.
As I already mentioned in the opening paragraph, most of the printing machines used between 15th and early 19th century were very similar and operated on a principle described above with small improvements, such as the knuckle lever installed in place of the screw, making the pressing stroke simpler and move even or the slow replacement of wood with cast iron as the main construction material, contributing to the longevity of all devices as well as to the miniaturization of a small-scale presses used to print leaflets and similar small-format publications. More complex models introduced in 1830s and 1840s had more elaborate systems, such as the ink rollers automatically spreading the ink on the matrix, limiting the necessary actions to positioning the sheets of paper and operating the crank, lever or pedal that set the machine cycle in motion. An example of the latter could be the Boston-type small-scale press build by Isaac Adams in 1830 and later adapted by him to use the steam power, effectively automatizing it. The first true innovation that is also the basis of most common offset printing machines to this day came however with the rotary machines in late first half of 19th century. These contraptions, of which the first known specimen has been built by Friedrich Koenig and Andreas Bauer in 1811 utilized the rotating cylinder. In the early models, rotating cylinder was used to press the paper sheet against the classical flat matrix, significantly improving the output of the machine.
First cylinder machine could produce roughly 800 prints per hour, but its next version using two cylinders and introduced in 1814 increased it to 1200 prints per hour. No wonder that the first customers of Koenig and Bauer were the newspaper publishers starting with the owners of the aforementioned London Times (just to compare, each issue of this daily newspaper was printed at the time in roughly 1500 copies).
The next crucial breakthrough came with the inventions of Augustus Applegath and Richard March Hoe who devised the way of putting the movable types into the rotating cylinder that was constantly inked by the ink feeder, limiting the actions of the printers other than maintaining the operation of the machine to rotating the cylinder (that soon was mechanized) and feeding the paper sheets, tremendously improving the output. Even early version of the Applegath's machine built in 1828 was able to print 4000 sheets per hour, two orders of magnitude more than the hand-operated presses ubiquitous several decades earlier.
So, to sum it up, the output of manually-operated simple flat-bed printing machine resembling the Gutenberg's press was very small in comparison with mid-19th century printing machines, not to mention modern ones, but it was still enough to produce a two dozens copies of an average book every day even when a single machine has been used and most printing shops used many presses to facilitate the production or make it possible to print several publications at once.