Remy Landau points out on his website hebrewcalendar.tripod.com the "Molad Zaqen Rule applies only to Rosh Chodesh of Kislev or Shevat of the previous year. Consequently, this rule is in no way related to the visibility of the new moon on Rosh Hashanah." Actually this statement is not entirely true and requires some analysis.
From the study done "2000 Years of Data" for the 2000 years before any consideration of dehiyyot:
75 times the Old Moon would be visible before dawn Erev Rosh HaShanah (3 day discrepancies).
These 75 times all have times of the Molad of Tishrei in the last quarter of the day. A visible Old Moon Erev Rosh HaShanah was indicative that any witnesses testifying to seeing the New Moon and so establishing the start of Rosh HaShanah was a false witness.
We know from our sources
120 CE Rabban Gamliel and Rabbi Yehoshua
198 CE R' Hiyya
358 CE Hillel b. R. Yehuda (Hillel II)
835 CE The Exilarch's Letter - Sacha Stern
922 CE Saadya Goan & Ben Meir
In the first four of these cases the Old Moon was actually seen and the application of the Molad Zaqen rule would have been useful to prevent a visible Old Moon Erev Rosh HaShanah. In the last case actually there was no visible Old Moon problem. Saadya Goan fought for a simple rule which eliminated the possibility of seeing the Old Moon Erev Rosh HaShanah perhaps because of his battle with the Karites. Karites could use a visible Old Moon Erev Rosh Hashanah as proof that the Rabbis were mishandling the calendar.
The Molad Zaqen rule defers all Rosh HaShanahs for which the Molad is in the last quarter of the day. Thus 25% of all years are deferred to solve a problem that affects only 3.75% of the years.