The Kollel wrote (in Insights to the Daf)-
>> The Mishnah describes how the witnesses who saw the new moon were cross examined and interrogated. The Mishnah later (24a) relates that Raban Gamliel kept models of the moon in different shapes and facing different directions in order to show the simple people who came as witnesses samples of how they saw the new moon. These Mishnayos clearly imply that the declaration of the new month was determined solely by authenticating the testimony of witnesses.
RABEINU BACHYE (Parshas Bo 12:2) cites a very interesting opinion in the name of RABEINU CHANANEL, which is also cited in the name of RAV SA'ADYAH GA'ON (see TORAH SHELEIMAH vol. 13, #293, and OTZAR HA'GE'ONIM to Beitzah, p. 3), that Kidush ha'Chodesh actually has nothing to do with witnesses. Rather, it is determined solely by the calculations of the Sod ha'Ibur given to Moshe Rabeinu at Sinai, with which the Beis Din calculates the new month every month. Witnesses did not affect the determination of the new month at all.
(b) The RAMBAM (Perush ha'Mishnayos) strongly rejects this explanation, for it contradicts many explicit statements in the Gemara. It is obvious that they were Mekadesh the Chodesh based on witnesses, and only when there were no witnesses did they do it based on calculations. The Rambam suggests that perhaps Rabeinu Sa'adyah wrote this opinion because of the Karaites in his time who were pestering him, saying that Kidush ha'Chodesh based on calculations is unreliable. In response, Rav Sa'adyah said that not only is Kidush ha'Chodesh based on calculations completely accurate, but Kidush based on witnesses is not even mid'Oraisa.<<
אמנם הרמב"ם כתב שרבנו חננאל כתב את דבריו רק כתגובה לקראים, אך לדעתי ניתן להוכיח שרס"ג סבר שכך הוא מעיקר הדין.רס"ג בספר המצוות שלו, מחלק את תרי"ג המצוות לא לרמ"ח ושס"ה, אלא גם למצוות המוטלות על היחיד ולמצוות המוטלות על הציבור (בית דין). והנה מצוות קידוש החדש נכללת במצוות המוטלות על היחיד.
והקשה ר' ירוחם פישל פערלא מהרמב"ם שמצוות קידוש החדש היא מצווה המוטלת על בית דין, ונשאר בצ"ע. אם רס"ג סבר שהעיקר הוא החשבון, א"כ מה שנאמר בקידוש חדשים הוא שעל כל אחד מישראל לדעת מתי חל ראש חדש על פי החשבון, וכתוצאה מכך מתי החגים, אמנם לב"ד יש זכות להתערב ולשנות אך זה עדיין לא משנה את ההגדרה הבסיסית שזו אינה מצווה ציבורית כי אם פרטית.
Although your idea is ingenious, unfortunately it creates more new problems than it solves.
1. The Mishnah in the beginning of Sanhedrin states that Kidush ha'Chodesh needs a Beis Din.
2. The Gemara (Rosh Hashanah 24a) brings a Pasuk to prove that the Rosh Beis Din must say "Mekudash."
3. From the Mishnah on 25a which relates the story of Raban Gamliel and Rebbi Yehoshua it is also clear that there must be a central [body determining] Rosh Chodesh.
These Halachos hold true (in some form) even when we are Mekadesh Al Pi Cheshbon. That is why the Rambam writes that is accepted that even when Rosh Chodesh is declared through calculation it is still only done by the Beis Din in Eretz Yisrael (Hilchos Kidush ha'Chodesh 5:1). If we accept your theory we will have yet another problem with the Shitah of RaSaG.
Dov Zupnik