How Big Should School Districts Be?

Lately, the question of "How big should a school district be?" has been on my mind as I reflect upon moving from a school that was 1700 students in size to one that is 2700+. The transition to this new, large building has been fairly smooth, but going from a place where I didn't know 10% of the staff to one in which I only know 10% has been weird. Increasingly, I had wondered if at 1700 the population of our school was too big and now with 2700 this question lingers.
Do school districts that have tens of thousands of students function at an optimal level given that there can be staggering differences (socio-economic, demographic, etc) between enrollment areas? If a school district has a common goal for all of its students wouldn't it be very difficult to allocate resources adequately if staggering differences exist?
It would be interesting to know what hurdles would have to be cleared if large school districts were to break up into more autonomous organizations that were able to focus and address the specific needs of its students and families. This approach might allow for enrollment/feeder areas to better align their educational programs and create better differentiated learning experiences. Not that this experience can't be replicated in a large scale organization, but how many students simply feel like a number or body in a class?
Obviously funding of such a model and a myriad of external challenges would exist, but imagine a system that would refocus the education on rigor, relevance, and relationships creating a better buy in from students and families who feel like humans rather than a number.