I guess it depends on the servers. I'm in academic/research computing and single-user systems are the anomaly. Part of it is having access to beefier systems for smaller slices of time, but most of it is being able to share data and collaboration between users.
If you're only used to cloud VMs that are setup for a single user or service, I guess your views would be different.
This is overwhelmingly the view for business and personal users. Settings like what you described are very rare nowadays.
No corporate IT department is timesharing users on a mainframe. It's just baremetal laptops or VMs on Windows with networked mountpoints.
Not a mainframe perhaps, but this sentiment is flat wrong otherwise, because that is how Citrix and RDS (fka Terminal Server) do app virtualization. It's an approach in widespread use both for enterprise mobile/remote access, and for thin clients in point of sale or booth applications. What's more, a *nix as the underlying infrastructure is far from unusual.
I have first-hand insider knowledge of two financial institutions that prefer this delivery model to manage the attack surface in retail settings, and a supermarket chain that prefers it because employee theft is seen as a problem. It’s also a model that is easy to describe and pitch to corporate CIOs, which is undoubtedly a merit in the eyes of many project managers.
One of the above financial institutions actually does still have an entire department of users logged in to an S/390 rented from IBM. They’ve been trying to discontinue the mainframe for years. I’m told there are similar continuing circumstances in airline reservations and credit card schemes; not just transaction processing, but connected interactive user sessions.
This is what corporate IT actually looks like. It is super different to the tech environments and white-collar head offices many of us think are the universal exemplar.