Be on-call. You need the sysadmins to be available to fix issues when they happen, even if the fixing itself takes little time.
> ... university lab ...
I developed a few web sites for universities, and they were hosted by the university. You really have to hope nothing breaks on Friday afternoon, or you have to wait until Monday morning to get it fixed...
You don’t remember correctly. There are multiple and to my knowledge there hasn’t been just one in at least the past ten years.
Buying and provisioning disks before space runs out is a small part of a DBA's job, and a modest constant-size task compared to predicting how fast space is running out.
In terms of your general point: it really depends on your business. In my last job there were 4 DBAs out of 12 total IT staff and they were constantly busy. In my current job there are no DBAs in a much larger team and yet no requirement to need one either. The two businesses produce vastly different products.
For more continuous workloads, you can overprovision on bare metal more cheaply to deal with the spikes.
Back when I worked at BT the unix developers all went on the basic sysadmin course from sun as part of their induction.
As an aside, this is one of the other reasons company directors like the cloud -- or serverless specifically: it absolves responsibility for hardening host infrastructure. Except it doesn't because you then need to manage AWS IAM policies, cloud watch logs and security groups instead of UNIX user groups, syslog and iptables (to name a few arbitrary examples). But that reality is often not given as part of the cloud migration sales pitch.
Clearly in the example above, you can afford to hire two sys admins to manage the bare metal servers (you can probably afford more, but 2 is the minimum that gives some peace of mind)
We had an application that was a glorified quiz engine and our customers would mass enrol and mass take the quizzes so the scaling that was offered by Azure made it a no brainer for us, specially as given the nature of our customers, quizzes would only take place during working hours, so we'd scale right down for half the day and scale up and out at peak times.
Total costs were about 1/2 of what we estimated for bare metal