"The rest of the story."
I alluded above to my previous experiences "in real life" (IRL). Here are the details:
I took my university's scuba course in 1986 when I was completing my terminal graduate degree, and became a TA for the course for several semesters until I graduated. I was one of the few TA's the instructor/professor allowed to man the fill station (including run the compressor). The course used Steel 72's exclusively at that time. At the time I took the course, the instructor already had been teaching this course that he, himself, designed, for many years.
Early in the instructor's tenure, there had been a catastrophic scuba compressor accident at a public university in an adjacent state. IIRC, someone--a university student, I believe--was either killed or maimed by an explosion of some sort. Because of this accident, my instructor was extremely safety cautious.
My instructor set up our fill station to consist of a government surplus Worthington compressor (intake air plumbed through the roof of the natatorium; manually-operated water separators after each stage; constant-flow, freshwater-jacketed lines between stages; a single, large filter stack that he packed manually, himself; over-pressure relief valve; etc.) connected to *six* cascade cylinders, themselves connected in series via pigtails. A single fill whip was connected to the first cascade cylinder. Scuba cylinders were filled in a water-filled garbage can.
I don't recall the exact characteristics of these cascade cylinders, but I remember they had a 3,500 psig service pressure.
Our rules were to fill the cascade system to a max pressure of 2,475 psig (2,500 psig, actually), and to fill the scuba cylinders to a max fill pressure of 2,250 psig--even though the instructor had all the scuba cylinders and the cascade bottles hydro-tested every *three* years, with the scuba cylinders tested for a "+" rating.
Each of our wet sessions had about 12 scuba students. (Six pool lanes, a buddy pair each lane.) So, potentially six "empty" tanks after each hour-long wet session. The fill station I describe above had sufficient capacity to fill all 12 scuba cylinders without recharge.
(Also, the compressor had high enough SCFM to top off the cascade system in less than an hour--so that the scuba cylinders could be refilled and used the next hour, by the next class. Typically, there were three hour-long wet sessions that met twice a week, with "optional" Sunday wet sessions.)
Clearly, the instructor had built layers of safety into his set-up: It was almost impossible to seriously overfill a scuba cylinder using his setup! (The OPV was set just north of 2,500 psig, IIRC.)
So, I kinda "knew" in advance that the above exercise would end with only a relatively few cascade cylinders being needed. Indeed, my intermediate calculations show that only six cascade cylinders (rather than eight) are needed if we had specified 12 Steel 72's (rather than 16) in the above exercise--consistent with my experience IRL.