Norma's situation is unique. She is permitted access to her market pizza stall only on Monday through Friday. She is not permitted to do anything with her dough off premises. She has to do everything on premises. She only makes pizza on Tuesdays, from about 8:30AM to about 8:30PM.
At the time that Norma decided to sell pizza at market, she had several possible options. For example, she could have made a cold fermented dough on Friday and used it about four days later (on Tuesday). Another possibility would have been to make a one-day cold fermented dough on Monday for use on Tuesday. I suppose she could also have made a one-day ambient temperature fermented dough, but the temperatures at market vary dramatically over the course of the year. After having tried a basic Lehmann NY style dough and found it wanting, she asked for help with something that would be better. I stepped forward and, shortly thereafter, the preferment Lehmann dough formulation was born. Ideally, it would have been nice to have used a poolish or similar preferment that was prefermented in the classic way, using small amounts of commercial yeast and a long prefermentation period at ambient temperature, or at a controlled temperature if that was possible. However, Norma was at the mercy of market temperatures and that ruled out a room temperature prefermentation (and a normal room temperature fermentation as well). The same conditions ruled out the use of natural starters and preferments. What we ultimately came up with was a poolish that was elaborated with a fair amount of flour, starting on Friday, and then cold fermented over the weekend until Monday, when she could go back to market to make the final dough. That dough would be cold fermented for use on Tuesday.
Preferments are like anything else. Some people like them and some don't. Some could do better with their preferments, but most people don't really understand them all that well, and even how they differ from each other (e.g., poolish vs. sponge vs. bigas vs old dough, etc.), and how to best use them. There are right ways to use preferments and there are wrong ways. All too often, people just make up their own preferments, and wonder why they don't work. I have always felt that it was a good idea to learn about preferments before using them. And, in that regard, I was fortunate to find articles about preferments that were written by Didier Rosada, formerly of the San Francisco Baking Institute. Those article can usually be found in the archives of the Wayback Machine at http://web.archive.org/web/20040814193817/cafemeetingplace.com/archives/food3_apr2004.htm
and at http://web.archive.org/web/20050829015510/www.cafemeetingplace.com/archives/food4_dec2004.htm
Even among professionals, preferments are uncommon. Other than Norma, the only professionals that I can think off offhand that use preferments are Brian Spangler of Apizza Scholls, Tom Douglas of Serious Pie, Anthony Mangieri of UPN and, apparently, Chris Bianco of Pizzeria Bianco.
Now, Norma is apparently at a crossroads. And I don't blame her for wanting to get out from under prefermented doughs if she can do so and meet the expectations of her customers. But the rules at market do not give her a lot of latitude. Unless she is able to control temperatures of fermentation, she realistically is left with a one-day cold fermented dough, made on Monday for use on Tuesday, or a four-day cold fermented dough, made on Friday for use on Tuesday. Or she could make and use frozen dough balls. I am sure that all of these options can be used successfully, and none would be unusual. In a pinch, where her doughs are unusable for some reason, she could make an emergency dough.
I am relying strictly on memory so Norma can correct me if I misstated anything about the rules at market and how they affect her.