I am viewing some of the comments, and have decided to answer them as posts. Blogger has a restriction on editing comments - even your own! It's quite annoying, but, the post is the work-around.
One of the questions asked is:
Is Mevarchim Chodesh for us the equivalent of Kiddush HaChodesh for our ancestors?
This is a great question. I pondered about this one some time ago. I found an excellent site that addresses various aspects of Jewish prayer, www.beureihatefilah.com. It has articles on so many topics. Almost all the articles are PDF files. One caveat - Often, I have discovered that articles contain "supplements" related to some topic other than what the link may have said. These supplements may serve useful interest in other areas. In short, the site author has done an amazing job, but, this is a small flaw.
Getting back to the question at hand, I am summarizing some ideas taken from this particular article from that site.
One of the original sources is Siddur Rav Amram Ga'on, about the 9th Century. It seems that the Yehi Ratzon opening prayer as well as the announcement of Rosh Hodesh was initially done after the Torah reading on Rosh Hodesh, itself. So, it seems clear that the announcement was not meant to commemorate the original Birkat Hachodesh - sanctification of the New Moon. Similarly, he cites various liturgical poems found as part of the Cairo Geniza, which als oindicate that one of these poems was recited as part of Grace after Meals on Rosh Hodesh - also indicating no connection to any announcement on the prior Shabbat.
Technically, what would actually be the reason to make any announcement of Rosh Hodesh if we assume that everyone in the world follows a fixed calendar and the date of Rosh Hodesh was known or could be easily found by just looking at the calendar?
There are 2 parts to this answer. The reason to announce in the first place is hinted to by Rav Amram Ga'on and it was done when Karaites, sticking to the strict law of the Torah, tried to convince everyone that the New Moon should be publicly declared only by sighting of the New Moon, as it had been done originally. As discussed, on my site, this system was changed at the end of the existence of the Sanhedrin around 4th Century C.E>, and from that time the fixed calendar was used. Thus, to counter the Karaites' cliaim, an announcement of Rosh Hodesh in synagogue was deemed necessary. Of course, this was initially done on Rosh Hodesh, itself, only as a public decleration to counter the Karaites.
I have listed just one source & reason mentioned in that article. There are other related reasons. Regardless, it was deemed necessary to publicly announce the date of Rosh Hodesh. Shabbat was most likely considered the best time to do so as this was a more asserted time when the public was likely to gather in the synagogue to hear this announcement.
