There's a huge difference between running an email server and some additional servers for thin clients -- all traditional stuff -- versus running an entire private cloud that redundantly stores the many many petabytes for your 40,000-person university, and all the web servers for the office software. Keeping it secure, keeping it updated, and having a live failover site if there's a fire or flood in your main data center that takes it out for weeks or months.

If it were that easy and cost-effective to do, large corporations would be doing it too. But there's a reason they're not.