Did early 20th century researchers state why they used E. coli as a model organism?
Historical Fallacies implicit in the Question


  
  “…why a researcher chose to use E. coli as a model organism.”
  


Researchers did not work with E. coli because they regarded it as a “model organism”. They worked with it because they were bacteriologists and it was a convenient bacterium to use. As Joshua Lederberg wrote in Microbiology Today (2004):


  From the beginning, although pathogenic strains were also found, E. coli was used as a representative, harmless bacterium that could be safely and easily cultivated even on synthetic media. On rich media, it will grow with a
  doubling time of 20 minutes; hence readily visible colonies can be seen overnight when it is plated on agar. Specialized media, like MacConkey’s agar,were developed for the selective isolation and identification of E. coli, as this was used as a global indicator for the pollution of water supplies. Hence, during the first half of the twentieth century E. coli was well known to bacteriologists. However, it was rarely, if ever, mentioned in general biology texts, as bacteria were generally regarded as pre-cellular in complexity and devoid of the nuclei and other genetic apparatus of ‘real’ organisms.


Indeed the term ‘model organism’ was not used in this sense until about 1970, as this Google ngram shows.


  
  “I imagine that prior to the widespread use of E. coli, scientists would have had to argue why they chose to use it to investigate biological phenomena not limited to this bacterium alone.”
  


You imagine wrongly. They were not sitting down and saying “we want to study this biological phenomenon, what bacteria shall we choose?” and certainly not having to justify themselves on publication. In general they published in specialized bacteriological journals where audience and referees would know why they were using E. coli or whatever. Even when Tatum and Lederberg (see below) published a letter on bacterial recombination in the general science journal, Nature, in 1946 they did not waste space on species justification:



No. You are imposing modern attitudes — governed by the contemporary state of science and its funding — upon the science of a completely different era. That is not the way to approach history.

Why did E. coli become the most studied bacterium?

It would seem that the discovery of bacterial recombination in E. coli by Lederberg and Tatum (for which they shared the 1958 Nobel Prize for Physiology or Medicine with George Beadle) was one of the key factors leading to the expansion in the use of E. coli (see Microbiology Today article previously cited). This phenomenon was originally suggested by studies on the transformation pneumococcal bacteria, but its demonstration in the bacterial workhorse, E. coli, opened the doors to the use of a wide range of genetic techniques that could be used for biochemical, as well as molecular biological, studies.