Here in Eretz Yisrael, we find Batei Hora'ah in many cities - places where a moreh hora'ah sits either during special times or perhaps the whole day or different rabbonim throughout the day answering shailos in all areas of Shulchan Aruch.
When did this all start? I'm looking to find any insights people might have for how this developed or any sources as well.
Once upon a time, I suppose, a beis medresh was enough because all of the chachamim were there. If someone had a shailo they went to the beis medresh. Nowadays, batei medreshim are filled with either avreichim in kollel, yeshiva bachurim, or baalei batim that spend some of their time learning. Generally no one in these groups of people would be qualified (or "certified") to answer shailos in halacha.
Perhaps this is why things changed? Along with the fact that a city used to have maybe one rov or each kehillah had a rov for themselves. In Yerushalayim alone I'm sure you could find 100s if not 1000s of people qualified to pasken shailos in practical halacha.