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.
Unis are more suited to do this than most corporations. For example at school i am at
1. They already self host many apps in production. Including their own complex homegrown app that manages the school. All of the students have 30 gigs of “network drive” for their virtual computer. That means lot of the infra is already there - including unified oauth/ldap.
2. There are already experts there teaching programming/devops. So these people can both administer and teach. I wouldn't underestimate inhouse capabilities.
3. It is quite easy to get grants for infrastructure modernization. These funds wouldn't be possible to use on paying third party services.
Overall I think its simply matter of costs and once googles/microsoft is not free they might not be the cheapest option anymore.
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.