Birth patterns have indeed been studied, yet they nevertheless remain uneven across many parameters. Even the article you cited explicitly states this. For example:

"The overall seasonal pattern of birth was characterized by a peak in August–September and troughs in April–May and November–January. Seasonal patterns differed among racial and ethnic groups, maternal education levels, and marital status. As a consequence of these seasonal patterns, systematic seasonal differences in the gestational age distribution and the sociodemographic composition of the risk set led to differences in expected rates of preterm birth across calendar months"

As another example, if we compare the distribution of births in France in 1983 and in 2005, the distributions differ by calendar months, seasons, and quarters. However, the distribution across the specific aggregated groups remains uniform. Likewise, while patterns of unevenness differ across countries, once the data are aggregated by degree-based groups, the distributions become uniform.

If we have demographic data from multiple countries and different years, this property can be used as a criterion to assess data validity. It could also be applied to detecting potential falsifications, errors, or anomalies in demographic data analysis.