A little research shows first that demographers (and others, such as epidemiologists, who report rates of events in human populations) do not "universally" use 100,000 as the denominator. Indeed, Googling "demography 100000" or related searches seems to turn up as many documents using 1000 for the denominator as 100,000. An example is the Population Reference Bureau's Glossary of Demographic Terms, which consistently uses 1000.
Looking around in the writings of early epidemiologists and demographers shows that the early ones (such as John Graunt and William Petty, contributors to the early London Bills of Mortality, 1662) did not even normalize their statistics: they reported raw counts within particular administrative units (such as the city of London) during given time periods (such as one year or seven years).
The seminal epidemiologist John Snow (1853) produced tables normalized to 100,000 but discussed rates per 10,000. This suggests that the denominator in the tables was chosen according to the number of significant figures available and adjusted to make all entries integral.
Such conventions were common in mathematical tables going at least as far back as John Napier's book of logarithms (c. 1600), which expressed its values per 10,000,000 to achieve seven digit precision for values in the range $[0,1]$. (Decimal notation was apparently so recent that he felt obliged to explain his notation in the book!) Thus one would expect that typically denominators have been selected to reflect the precision with which data are reported and to avoid decimals.
A modern example of consistent use of rescaling by powers of ten to achieve manageable integral values in datasets is provided by John Tukey's classic text, EDA (1977). He emphasizes that data analysts should feel free to rescale (and, more generally, nonlinearly re-express) data to make them more suitable for analysis and easier to manage.
I therefore doubt speculations, however natural and appealing they may be, that a denominator of 100,000 historically originated with any particular human scale such as a "small to medium city" (which before the 20th century would have had fewer than 10,000 people anyway and far fewer than 100,000).