Do school districts need their own data centers anymore? Yes and no, They still need a connection out to the internet, as well as a firewall for security, and then distribution of the internet connection to each school. But, do they need anything more than that?
My school district has a multi-million dollar data center to support 41 buildings, 21,000 students and over 4,000 faculty and staff. Above is just two of the 10 racks in the data center. It's expensive to maintain (engineer, air conditioning, power) and can fail. There are lots of servers and a left hand setup for files and databases, along with appliances for different types of software. However, much of it is legacy now. In addition, you need to backup all of your data, preferably offsite.
Schools are turning more toward web services, even our district. Google Apps, Evernote, Edmodo, and more are all web based. PowerSchool, Destiny and other services that used to be local servers are now hosted by the vendors. E-rate no longer pays for servers either.
So, can school districts just provide internet connections and routings to each building? I think most can. Save the money from a data center and use it for faster switches, more WiFi and increased internet bandwidth. Let vendors handle issues and maintain their own servers. Make sure they back up your data to multiple locations.
We use Backupify to backup and archive all of our Google Apps data and the other vendors backup the data to multiple locations. We are still maintaining some systems and file servers, as well as an Exchange server, but most school systems can get away from that.
I was just speaking with a smaller school district that is looking to revamp their entire technology. They are moving to Google Apps and Chromebooks (and moving all files to Drive) and are moving to have Pearson host PowerSchool instead of hosting themselves. By the end of the summer, they will not host any systems or software and will focus on increased bandwidth and wireless access in the district. The money savings will also be used to buy more student devices.
In today's web based world, servers and hosting your own systems seems outdated.
UPDATE: I forgot to mention one thing - make sure you have a backup internet connection. Our district has three distinct internet connections so that if any one POP goes down, or a cable goes down, we still have a connection. Some schools use 4G connections as a backup too.